Over July 4th weekend in Las Vegas, Griffin O'Neal, 24, married his live-in lady love of the past two years, Rima Uranga, 28. For Griffin, son of 48-year-old actor Ryan O'Neal, it was an all-too-rare joyous occasion in a trouble-plagued life. And if the happy couple's choice of venue—the nation's gambling capital—wasn't exactly romantic, it was apt: Every marriage is a game of chance.

Griffin and Rima, a hairdresser, wearing smiles as brilliant as the neon-lit sky, exchanged their vows before a small group of friends and family at the Candlelight Wedding Chapel. The ceremony cost all of $45, but Rima's dad plunked down a few extra bucks for flowers, photographs and a limo. Afterward, the party moved to the Dunes hotel, where Papa Ryan—who attended without Farrah or daughter Tatum—had arranged for a surprise reception including a three-tier cake and champagne.

Griffin and Rima met two years ago at Duke's, a popular Sunset Strip breakfast spot. "It was love at first sight," she recently told a reporter for Fame magazine. It would have had to have been some sort of powerful emotion for, as Griffin put it during the same interview, "Before Rima, I don't think I had a girlfriend for longer than seven or eight days." Soon she moved into his two-bedroom North Hollywood apartment, where they set up housekeeping with three dogs, two cats, a parrot and a snake named Cornelia. O'Neal has called Uranga, not without affection, "the thorn in my butt... She's my drill sergeant. But it's positive and it's good." As for Rima, she has said, "There is a misconception that Griffin is a crazy, wild and uncaring boy,...but he has a heart of gold."

Certainly O'Neal's troubles with drugs and his nearly two-year stay at Habilitat, a boot-camp type rehabilitation program in Hawaii, are well known. Likewise his intensely competitive, often violently strained relationship with his father—who once punched out two of Griffin's front teeth—and his role in the speedboat death of Gian Carlo Coppola, son of director Francis Ford Coppola, three years ago. O'Neal insists he has been changed by the death of Gian Carlo—and made better by the ordeal. Rima seems to agree. "In the past couple of years, Griffin has matured a lot," she has said. At least that's what she bet in Vegas.