In 1976, after his retirement, Angleton told an investigator that he knew which mob figures, from the New York and Chicago mafia families, had killed Sam Giancana. He also blamed the Church Committee for causing the death of Giancana and Rosselli, by demanding testimony concerning topics on which the mafia code of silence could not be broken.

Exner's account cannot be dismissed. It is specific in dates and details and supported by travel documents, by her annotated appointment book, and by official logs recording three of her visits to the White House. A credible source has said Exner told him the gist of her story soon after the events in question. Giancana's half-brother Chuck has also claimed to know of contacts between the mafioso and Kennedy, and of the go-between role played by Exner.

Meanwhile, a source far more likely to be believed has stated that Robert Kennedy, supervising anti-Castro operations for his brother, ordered the CIA to assign a case officer to meet with Mafia figures. Sam Halpern, a former senior Agency official on the Cuba desk, said Kennedy himself supplied the Mafia contacts.

If such allegations - and especially Judith Exner's claims - are true, then President Kennedy was playing a horrendously dangerous game. For, throughout the presidency, his brother was vigorously pursuing his investigation of the Mafia - not least of Giancana himself. Giancana and other top mobsters evidently hoped for leniency under a Kennedy administration, as a quid pro quo for their support during the election that brought Kennedy to power. But Giancana would be overheard on an FBI wiretap saying, "The President will get what he wants out of you... but you won't get anything out of him."

If top Mafia bosses now felt double-crossed, their law - the law of the mob - might demand vengeance.

Judith Campbell Exner, who has died of cancer, aged 65, in a Los Angeles hospital, became notorious in the middle 1970s when she claimed that she had had an affair with President John F Kennedy from 1960 until 1962. She said she and Kennedy made love in New York hotels, at Kennedy's home and even in the White House. After her affair with the president ended, she had a brief relationship with Sam Giancana, the capo of the Chicago Mafia.

In her 1977 memoirs, My Story, she described how she arranged a meeting between Kennedy when he was running for the presidency and Giancana in April 1960, as a result of which the mobster sent an aide, Paul "Skinny" D'Amato, to West Virginia to buy support for Kennedy in the Democratic Party primary election there. She also hinted that Giancana had helped Kennedy carry Illinois, which he won by a few thousand votes in the Chicago area.

For many years, rumours circulated that Judith Campbell had also been involved in a plot hatched between her two lovers, Kennedy and Giancana, to kill the Cuban leader, Fidel Castro. In 1991 she came forward and described how she had sat on the edge of the bathtub in a Chicago hotel while the president and the Mafia don talked in the bedroom.

In April, with Jackie Kennedy away in Florida, Campbell was seeing Kennedy at his house on N Street in Georgetown, the upmarket Washington DC suburb. One night Kennedy asked Campbell to put him in touch with Sam Giancana, and within the week JFK was meeting the mafioso at the Fontainebleau Hotel in Miami Beach to arrange mob help with his Democratic primary campaign in West Virginia. After the break-up of her affairs with Kennedy and Giancana, Campbell was afraid for her life and kept her archives under the bed at her house in Newport Beach, California, guarded by a large dog, with a pistol under her pillow.

Kennedy's involvement with the Mob in a plot to kill the Cuban president has often been put forward as one of the reasons for his own assassination in Dallas in November 1963.

In the winter of 1959-60, however, the CIA still thought it could pull off the invasion (of Cuba). But it thought the odds might be better if the plan went one step further - the murder of Fidel Castro. All the Company needed was someone to do the dirty work for it. Professional killers. A gangland-style hit.

It was then that the CIA conceived the notion to let the mobsters do it themselves. They'd had a grudge against Castro ever since he'd forced them out of the Havana casinos. It was even rumored that Meyer Lansky had put a million-dollar bounty on Castro's head. CIA Director Alien Dulles passed the ball to his deputy director, Richard Bissell. Bissell handed off to the CIA security chief. Colonel Sheffield Edwards. And then I received the call...

Though I'm no saint, I am a religious man, and I knew that the CIA was talking about murder. O'Connell and Edwards contended that it was a war - a just war. They said it was necessary to protect the country. They used the analogy of World War II: if we had known the exact bunker that Hitler was in during the war, we wouldn't have hesitated to kill the bastard. The CIA felt exactly the same way about Castro. If Fidel, his brother Raul, and Che Guevara were assassinated, thousands of lives might be saved.

But in my mind, justified or not, I would still have blood on my hands. I had to think about it. The deal carried a pretty big price tag. I kept thinking about my family. What kind of danger would it put them in? If anything went wrong, I was the fall guy, caught between protecting the government and protecting the mob, two armed camps that could crush me like a bug....

Rosselli's first response was laughter. "Me? You want me to get involved with Uncle Sam? The Feds are tailing me wherever I go. They go to my shirtmaker to see if I'm buying things with cash. They go to my tailor to see if I'm using cash there. They're always trying to get something on me. Bob, are you sure you're talking to the right guy?"

When I finally convinced Rosselli that I was serious, very serious, he sat staring at me, tapping his fingers nervously on the table. I didn't want to pull any punches with the man, so I was totally up-front about the conditions of the deal.

"It's up to you to pick whom you want, but it's got to be set up so that Uncle Sam isn't involved - ever. If anyone connects you with the U.S. government, I will deny it," I told him. "If you say Bob Maheu brought you into this, that I was your contact man, I'll say you're off your rocker, you're lying, you're trying to save your hide. I'll swear by everything holy that I don't know what in hell you're talking about."

Rosselli hesitated at first, but then agreed. Many people have speculated that Johnny was looking for an eventual deal with the government, or some sort of big payoff. The truth, as corny as it may sound, is that down deep he thought it was his "patriotic" duty.

Understand that the world was quite different then. The Cold War was raging. Only months before, Francis Gary Powers had been shot down while flying his U-2 reconnaissance plane over the Soviet Union. The relationship between Washington and Moscow was at an all-time low, with Soviet Premier Khrushchev going so far as to openly call President Eisenhower a liar on several occasions.

Once the decision was made, it didn't take Rosselli long to put his plan into motion. On October 11, 1960, we took off for what would be the first of many trips to Miami. We booked ourselves into the Kenilworth Hotel, selected because Arthur Godfrey did his TV show from there. In Miami, Johnny introduced me to two men who would help us - "Sam Gold" and "Joe." Sam was Johnny's backup man; Joe would be our direct contact in Cuba. These weren't ordinary mob lackeys. Johnny didn't bother to tell me that "Sam" was Sam Giancana, his boss within the Mafia and the chief of its gigantic Chicago operation. Or that "Joe" was Santos Trafficante, former syndicate chief in Havana, and the most powerful Mafia man in the South.

I later learned that Johnny didn't just need a little help from these men, he needed their okay. Trafficante was necessary to get Castro because he had the connections inside Cuba, and Giancana was necessary to get Trafficante, because Trafficante had the stature of a "Godfather," and only a man of equal stature - like Giancana - could approach him for help. Johnny couldn't do it on his own. Both were among the ten most powerful Mafia members - a fact I learned only after seeing their pictures in a magazine soon after meeting them.

The CIA's Sheffield Edwards was supposed to make the contact with the underworld. He approached a former FBI agent and CIA operative, Robert Maheu, who moved at the subterranean level of politics. Maheu knew his way around the shady side of Las Vegas; he had been recruited by billionaire Howard Hughes to oversee his Las Vegas casinos. Happily, Hughes was a friend who owed me a favor. Intermediaries persuaded Maheu to confide in me. He confirmed that the CIA had asked him to sound out the Mafia, strictly off the record, about a contract to hit Fidel Castro. Maheu had taken the request straight to Johnny Rosselli.

Rosselli had a reputation inside the mob as a patriot; he was quite willing to kill for his country. But as he told me, there was an etiquette to be followed in these matters. Santo Trafficante was the godfather-in-exile of Cuba after Castro chased out the mob. Rosselli couldn't even tiptoe through Trafficante's territory without permission, and he couldn't approach Trafficante without a proper introduction. So Rosselli prevailed upon his boss in Chicago, Sam "Momo" Giancana, to attend to the protocol. Since Giancana had godfather status, he could solicit Trafficante's help to eliminate Castro. The project appealed to Giancana who had commiserated with other dons over the loss of casino revenues in Havana. Killing Castro for the government would settle some old scores for the mob, and it would put Uncle Sam in the debt of the Mafia.

Maheu had been ordered to keep a tight lid on the involvement of the U.S. government. The CIA was ready with a cover story that the Castro hit had been arranged by disgruntled American businessmen who had been bounced out of their Cuban enterprises by Castro.

On September 25, I960, Maheu brought two CIA agents to a suite at the Fountainebleau Hotel on Miami Beach. Rosselli delivered two sinister mystery men whom he introduced only as Sicilians named "Sam" and "Joe." In fact, they were two of the Mafia's most notorious godfathers, Sam Giancana and Santo Trafficante, both on the FBI's ten-most-wanted list. They discussed the terms of Castro's demise, with Giancana suggesting that the usual mob method of a quick bullet to the head be eschewed in favor of something more delicate, like poison.

The wily Giancana was less interested in bumping off Castro than in scoring points with the federal government, and he intended to call in as many chips as he could before the game was over.

From Chicago, Mooney brought in Richard Cain, Chuckie Nicoletti, and Milwaukee Phil, all having worked previously on "the Bay of Pigs deal". Mooney said that both Cain and Nicoletti were actual gunmen for the hit, being placed at opposite ends of the Dallas Book Depository, In fact, he asserted it was Cain, not Oswald who'd actaully fired from the infamous sixth story window.

Of the Mafia trio, only Roselli testified before the State committee. On July 19, 1975, the night before he was going to be questioned by committee members, Sam Giancana was preparing a supper... when a person he evidently trusted and had invited to share the meal ended his life by firing a .22 caliber handgun equipped with silencer into the back of his head. The killer followed up by discharging six more rounds into Giancana's neck and mouth.

Some organized-crime experts theorized that Giancana's murder was unrelated to the Senate inquiry, and that he was killed by rivals to stop him from regaining supremacy of Chicago's Mafia clan. From what I had picked up over the years about mob executions, the nature of Giancana's death contradicts that theory. In a traditional Mafia hit, a bullet in the throat signifies that the victim had been 'talking,' and a bullet in the mouth means he will never 'rat' again. Undoubtedly, Giancana was murdered to prevent him from talking about the CIA-Castro plot or any other Mafia secret.

Almost exactly on the first anniversary of Giancana's death, another layer of mystery was added to the coincidence of his slaying and the Senate's CIA investigation. After years of seemingly cooperating with congressional committees and talking rather freely with newspaper columnists about Mafia affairs, Johnny Roselli became extremely cautious, almost reclusive...

In late July 1976, Roselli made a dinner date. He was seen with his old friend Santo Trafficante at The Landings, a restaurant in Fort Lauderdale. Two days after dining with Santo, Roselli disappeared.

Twelve days later, on August 7, 1976, a fifty gallon drum containing the legless body of a silver-haired man... The corpse was Johnny Roselli.

The manner of Roselli's death also fit a Mafia pattern. He was beguiled to his death by someone he trusted. The dumping of his body in the bay was another message: The killers either wanted to give the impression that he had deliberately vanished or they wanted to punish his relatives for his misdeeds, perhaps his violation of omerta...

One fact, however, was indisputable: Santo Trafficante was the only survivor of the three mobsters recruited by the CIA to kill Fidel Castro.

The Mafia had strong reasons for wanting Kennedy dead. They had lost their huge gambling interests in Havana when Castro seized power, and had been standing on the touchline waiting for action by die Kennedy administration which would reverse the situation and give them their casinos back. It never happened. Instead they watched their government embrace a policy of détente towards Castro's Cuba with growing dismay and anger. Nor was this the only reason for their disenchantment with Kennedy. John appointed his brother, Robert, Attorney General, and Robert had opened up an all-out war against the Mafia. Never before had such success been obtained by the forces of law against mobsters who, for years, had evaded prosecution. It had also a gathering momentum, for law enforcement agents in many cities in the United States were so impressed by Robert Kennedy's campaign they began bringing cases against their local mobsters which past experience of failures had made them reluctant to prosecute. The local success rate also boomed, and the Mafia were shaken. Their instincts were to kill Robert Kennedy, but they knew that this would only cause the President to increase the pressure, leaving the only way to kill the President. If the President was removed, the Attorney General would be replaced, since the appointment was one of patronage.

Chicago mobster, Sam Giancana, was high on Robert Kennedy's hit list, and he was well aware of it. He claimed to have had connections with the Kennedy's father, Joe, who made his fortune as a bootlegger in the days of prohibition. His dealings with Joe Kennedy, he claimed, earned him privileges from the President rather than the persecution to which he was being subjected. In a book. Double Cross: The Story of the Man Who Controlled America, published in Britain in 1992, Sam Giancana's brother and nephew sought to establish that Giancana had rigged the Presidential election vote in Cook County on John Kennedy's behalf, which effectively gave Kennedy the election. This was to ensure a 'relationship' between the President and Giancana, on which the President reneged, and Giancana killed the President for his double cross. It is a spicy, imaginative tale for which no substantiation is provided at any level.

A favorite theory of many JFK assassination buffs is that the mob, led by Chicago boss Sam Giancana (pictured right), ordered a hit on the president as payback for double-crossing them after they helped him win the 1960 presidential election. When Kennedy won Illinois, many Richard Nixon supporters claimed that then-Mayor Richard J. Daley's political machine in Chicago had fixed the city election, thus helping Kennedy carry the state. But others, most notably investigative reporter Seymour Hersh in his 1997 book, The Dark Side of Camelot, have claimed that instead of mere dirty politics, JFK, or more likely his father Joseph, a former bootlegger, made a deal with Giancana to swing crucial wards in the city. Giancana's son and grandson make a similar claim in their book, Double Cross, and of course, Oliver Stone could never make enough connections between the mob and the assassination in his film, JFK. After he was elected, JFK's brother and attorney general Bobby started a campaign against organized crime, enraging mob leaders like Giancana who thus wanted to see him dead.

Why the history lesson? Well, Chicagoist loves a good JFK assassination theory, so we perked up when we saw the Sun-Times reporting that UIC finance professor John Binder recently analyzed vote totals from in the 1960 general election in city wards where Giancana supposedly had clout to see if the mob really did swing the election. And he found that the mob-controlled areas in the city, as well as Cicero and Chicago Heights, voted no differently than others. In fact, Democratic vote totals remained about the same in those wards for Kennedy in 1960 as they were for Adlai Stevenson in 1956. Binder also disputes the notion that Giancana helped Kennedy win the state of West Virginia, and that the mob influenced citywide votes via union support.

So if JFK didn't owe Giancana any favors for helping him win Illinois, would Bobby's crusade against the mob still have angered them enough to order a hit on the President? Maybe. But if not, conspiracy nuts always have a host of other favorite suspects, including anti-Castro Cubans, some guy named Lee Harvey Oswald, the Soviets, Texas oilmen, and Lyndon Johnson himself. The parlor game never ends no matter how bizarre the idea. But if Professor Binder is right, you can take some of the major Chicago ties out of the equation.