Last month LIFE posted 20 unpublished photos of Steve McQueen just hanging out in his free time. They feature McQueen doing all the things you would think he would do in his free time. As GQ put it, "LIFE just unearthed 20 candid photos of McQueen doing exactly what you imagined him doing off-set: chugging beers, playing with guns, practicing his jabs at the gym, shamelessly breaking public deceny laws, and speeding in cars like nobody's business. Check it out".
In the spring of 1963, Steve McQueen was on the brink of superstardom, 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. 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 see what he could get. Three weeks and more than 40 rolls of film later, Dominis had captured some astonishingly intimate and iconic images, photos impossible to imagine in today's restricted-access celebrity world. Only a handful of those photos have ever been published… but now, in celebration of what would have been McQueen's 80th birthday (March 24), LIFE.com presents these never-before-seen gems from that legendary assignment, along with insights from Dominis about the time he spent with the man who would become known as the King of Cool.