In a gallon-size resealable plastic bag, combine the yogurt, garlic, cumin, chili powder and 1/2 teaspoon each salt and pepper. Cut 2 slashes in each chicken breast through to the bone and add to the yogurt mixture; turn to coat. Refrigerate for 30 minutes.
Preheat the oven to 450 degrees . Place the chicken on a rack set over a rimmed baking sheet and roast until cooked through, about 30 minutes.