Photos of Steve McQueen and Neile Adams by LIFE, 1963

"We went on a weekend drive, after a show I was in at the time. We were on a motorcycle, and there was a carload of friends behind us. It was freezing ass cold. We stopped for a bite to eat, and one of the guys said, ‘Steve, why don’t you let Neile ride with us? I can ride with you. It’s too cold.’ And I said, ‘No, I think I’m just gonna stay on the bike.’ Steve told me later, ‘That’s the moment I fell in love with you.' "—Neile Adams