Whisk together all of the ingredients except the chicken. Reserve 1/3 cup of the marinade for basting. Place the chicken and remaining marinade in a resealable plastic bag. Make sure the chicken is coated and remove as much air from the bag as possible. Seal and refrigerate for 8-24 hours.
Preheat grill to medium (or oven to 350 degrees F). Drain marinade from chicken and discard. Grill chicken pieces, basting once or twice, for about 40 minutes (bake for 50-60), or until a meat thermometer registers 170 degrees F.