In July 1969, Senator Ted Kennedy is asked in an interview how it feels to stand in the shadow of his dead brothers John and Bobby. Then he phones his cousin Joe Gargan and tells him to book hotel rooms on Martha’s Vineyard for the Boiler Room Girls, who worked for Bobby’s presidential campaign. He travels to Chappaquiddick Island, where he meets with Gargan and Paul Markham for a sailboat race. After losing, Kennedy goes to a party at a cottage with five friends and six Boiler Room Girls.

Kennedy leaves the party with Mary Jo Kopechne. On the road, they encounter a police officer, who asks if they need help. Kennedy backs up and drives quickly away. He accidentally drives off the Dike Bridge, causing the car to flip over before it submerges into a pond. Kennedy climbs out of the vehicle, and calls out to Kopechne, but receives no response. He sits down and cries, before walking back to the cottage. He summons Gargan and Markham, and they drive quickly to the bridge. Gargan and Markham attempt multiple times to retrieve Kopechne from the overturned vehicle, but are unable to open any of the doors or windows. They insist Kennedy report the incident immediately, but instead, he gets in a rowboat, and Gargan and Markham row him to Edgartown, where they go their separate ways.

Kennedy walks past the phone booth outside his hotel and up to his room and gets undressed. He takes a bath, gets dressed, and combs his hair. He goes down to the phone and calls his father Joseph P. Kennedy Sr. for advice. His partially-paralyzed father says one word: “alibi.” Kennedy sits on the steps outside his room. He asks the night porter the time, which is 2:25 a.m. Kennedy claims he is having trouble sleeping, but he goes to sleep without contacting the police.

The next morning, the overturned vehicle is discovered by father-and-son fishermen, who call the police. Police Chief Arena and the fire department recover Kopechne’s body from the car, which they find is registered to Kennedy. Gargan and Markham realize that he has not reported the accident, and insist again that he must. Kennedy goes with Markham to the Edgartown Police Department and commandeers the Chief’s office, waiting for his return.

After giving the Chief a statement written by Markham, Kennedy travels to the family compound in Hyannisport, believing he has contained the situation. He is shocked as his father tells him his actions have disgraced the family, and is surprised by a damage control team led by Robert McNamara, convened to address the legal (potential charge of manslaughter) and political problems. First they make sure the body is not examined again, and that the official record that his license has expired is changed by a Kennedy-friendly official. Then they craft a strategy to push the court hearing after the current news cycle, dominated by the landing of the first men on the Moon. Kennedy attends Kopechne’s funeral wearing a neck brace to gain sympathy, but this ploy backfires in the press.

Kennedy suggests an appeal to the people of Massachusetts on national television, which his damage control team heartily endorses. They use the family’s influence to resolve the court case without a trial, where anything he says publicly could be used against him. Kennedy gets the minimum sentence by pleading guilty to leaving the scene of an accident: two months jail time, which the judge suspends based on Kennedy’s character and good standing.

Gargan, who has become increasingly disgusted with Kennedy for not being honest about the facts of the case and attempting to play the victim, attempts to resign. Kennedy, having just been slapped by his father, tells Gargan he intends to resign from the Senate and asks him to draft a resignation speech. He tells Gargan not to tell anyone.

As Kennedy is ready to go on national television with the speech prepared by Ted Sorensen, designed to elicit public sympathy, Gargan gives Kennedy the resignation speech, telling him it is the right thing to do. But Kennedy throws it away, and Gargan is pressed to hold Kennedy’s cue cards for Sorensen’s speech. Although the public has mixed views, the majority interviewed say they would re-elect him.

The credits explain that Joseph Kennedy Sr. died soon after the incident; Gargan became estranged from the family; and Kennedy lost the 1980 Democratic Party presidential primaries but continued in the U.S. Senate for another 40 years after the incident.