When ready to cook chicken, heat gas or charcoal grill. When grill is heated, carefully oil grill rack. Remove chicken from marinade; reserve marinade. Place chicken on gas grill over medium heat or on charcoal grill over medium coals; cover grill. Cook 12 to 15 minutes, turning occasionally, until juice is no longer pink when centers of thickest pieces are cut and thermometer inserted in centers reads 170°F.