Mix together yogurt, oil, lemon juice, garlic, ginger, and spices.
Make diagonal slashes in the chicken meat to allow marinade to penetrate better. Pour yogurt mixture over chicken parts.
Marinate for 4 hours at room temperature, or overnight in the refrigerator, turning occasionally. If the chicken is placed in the refrigerator, bring it to room temperature before cooking (approximately 1 hour).
Brush grill or shallow baking pan with a little oil to keep chicken from sticking. Arrange chicken on the pan.
Broil chicken 2-3 inches away from the heat until cooked through, approximately 25 minutes, turning halfway through.
Serve hot with basmati rice or naan (Indian flatbread).