He was one of only two men, along with Paul Markham, in whom Ted Kennedy chose to confide immediately after the Chappaquiddick automobile accident which killed Mary Jo Kopechne.
Gargan fell out of favor with the Kennedy family in 1988, with the publication of journalist Leo Damore's book, Senatorial Privilege: The Chappaquiddick Cover-Up, because Gargan revealed in interviews with Damore details not released in public testimony, such as how Ted Kennedy contemplated covering up his role in the incident by claiming Kopechne was driving his car.
For college, Gargan chose to attend Notre Dame as his father did, rather than Harvard as Joseph Kennedy and all of his sons did.
Markham seconded this opinion, but Kennedy argued against it, and according to Gargan, said he could plausibly deny knowledge of the accident if they agreed that he had gotten out of the Oldsmobile beforehand and Kopechne was the one who drove it off the bridge.
According to Gargan, Kennedy then abruptly cut off the discussion by jumping into the channel and swimming the 500 feet to the Edgartown shore.
Later, Kennedy used Gargan's and Markham's status as lawyers to falsely assert attorney-client privilege, preventing them from saying anything about the conversation on the island.
[9] In 2020, his son, Joseph E. Gargan, pleaded guilty "to embezzling nearly $8 million that was intended to settle claims by children who alleged they were victims of medical malpractice".