Combine all ingredients (except chicken) for marinade (may be processed in a blender). Set aside 1/2 cup of this marinade in a clean jar (do not use the 1/2 cup set aside to marinate chicken - this portion will be used for basting the chicken during the grilling). Keep refrigerated.
Put marinade into a Ziploc bag with chicken pieces and distribute evenly. Marinate chicken for 6-12 hours in refrigerator, turning occasionally.
Remove chicken from marinade and drain. Allow to sit at room temperature while grill heats up. Grill over medium high heat (grill open) for 5 minutes, then close grill and reduce heat; continue cooking over low heat, for 15-20 minutes, or until chicken is done (juices will run clear when pierced with a fork). Baste with 1/2 cup fresh marinade every few minutes, turning chicken to cook both sides evenly.