In 1-gallon resealable heavy-duty plastic food-storage bag, mix all ingredients except chicken. Add chicken; seal bag and turn to coat with marinade. Refrigerate at least 1 hour but no longer than 24 hours, turning bag occasionally, to marinate.
Heat gas or charcoal grill. Remove chicken from marinade; discard marinade.
Place chicken, skin sides up, on grill over medium heat. Cover grill; cook 15 minutes. Turn chicken. Cover grill; cook 20 to 40 minutes longer, turning occasionally, until juice of chicken is clear when thickest piece is cut to bone (170°F for breasts; 180°F for thighs and drumsticks).