They met on the set of Playing God in May 1996.
From Celebitchy and Star Magazine:
"Star Magazine does some detective work to try and figure out who the fourth guy was that Angelina had sex with. Angelina is quoted recently in British Cosmopolitan as saying that “I had only slept with four men in my life - and I married two of them!”
That doesn’t mean it’s true, just that she may have said it.
Star speculates that her mystery lover was Timothy Hutton, who she met on the set of Playing God in 1997. She had something that looked like an “h” tattooed on her wrist at the time, and people said they were an item. Angelina says the “h” is for her brother, James Haven.
[From Star Magazine, print edition, October 8, 2007]
"Star can reveal that all signs point to actor Timothy Hutton as Angie’s mystery man! When the pair costarred in the 1997 thriller Playing God, there were whispers that they were an item. These rumors escalated when a tattoo of the letter H - for Hutton - appeared on the inside of her wrist.
Later Angelina, now 32, insisted the “H” was for her brother James Haven, not Timothy, 47. So why won’t Angelina admit that it was Timothy? He was divorced from actress Debra Winger at the time.
When she and Timothy broke up, Angie took it hard, the source says. “Angie was very in love with Timothy and wanted to get serious, but he didn’t,” says the insider. “He broke her heart, and that led to a downward spiral for her in terms of her mental health.” The insider adds that after the split, Angelina turned to women and experimented with heroin."