In large bowl or resealable food-storage plastic bag, mix all ingredients except chicken. Add chicken; turn to coat. Cover bowl or seal bag; refrigerate at least 1 hour or up to 4 hours to marinate.
Heat gas or charcoal grill. Remove chicken from marinade; reserve marinade. Place chicken, skin side down, on grill over medium heat. Cook 10 minutes.
Brush chicken with marinade; turn chicken. Cook 20 to 30 minutes longer, turning and brushing frequently with marinade, until juice of chicken is clear when thickest piece is cut to bone (170°F for breasts; 180°F for thighs and legs). Discard any remaining marinade.