In large shallow glass dish or 2-gallon resealable food-storage plastic bag, mix all ingredients except chicken. Add chicken; turn to coat with marinade. Cover dish or seal bag and refrigerate, turning chicken occasionally, at least 3 hours but no longer than 24 hours.
Heat gas or charcoal grill. Remove chicken from marinade; reserve marinade. Place chicken, skin sides up, on grill. Cover grill; cook over medium heat 15 to 20 minutes.
Turn chicken. Cover grill; cook 20 to 40 minutes longer, turning and brushing 2 to 3 times 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.