Mince 1 clove garlic; smash the rest. Combine the garlic with the vinegar, olive oil, oregano, chiles and 2 teaspoons salt in a large bowl. Add the chicken and toss to coat. Cover and refrigerate for at least 2 hours or overnight.
Preheat the oven to 450. Arrange the chicken in a roasting pan; roast until cooked through and golden, about 30 minutes. Garnish with oregano. Brush pita bread with the pan drippings to serve with the chicken.