A.J. Foyt, 84, is a retired race-car driver and current IndyCar team owner who was the first to win the Indianapolis 500 four times. He also is the only driver to win the Indianapolis 500, the Daytona 500 and the 24 Hours of Le Mans. He spoke with Marc Myers.

When I was 15, my father gave me a new 1950 two-door black Ford to work on. I souped it up so the car was really fast—so fast that I could outrun the cops in the West University section of Houston.

Three weeks later, the police there summoned me to the station. They asked me about the Ford. I told them someone must have stolen it and was speeding.

The officers said they talked to my friends and knew all about it. I said, “Well, just put me in reform school then, ’cause I know what my daddy is going to do to me when he comes to get me.”

When my father picked me up, the officers told him that he had a good boy and that they’d let me go provided he didn’t lay a hand on me.