In small bowl, combine all ingredients except chicken; mix well. Place chicken in large shallow nonmetal dish. Brush or rub oil mixture on chicken pieces, using all of mixture. Cover; refrigerate at least 1 hour to marinate.
Heat grill. When ready to grill, remove chicken from marinade; reserve any remaining marinade. Place chicken on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 30 to 40 minutes or until chicken is fork-tender and juices run clear, turning and brushing with marinade 2 or 3 times. Discard any remaining marinade.