In the spring of 1963, already popular from his big-screen breakout as one of The Magnificent Seven and just a couple months away from entering the Badass Hall of Fame with the release of The Great Escape, Steve McQueen was on the brink of superstardom.

Intrigued by his dramatic backstory and his off-screen exploits — McQueen was a reformed delinquent who got his thrills racing cars and motorcycles — LIFE sent photographer John Dominis to California to hang out with the 33-year-old actor and, in effect, see what he could get.