In a small bowl, whisk the first 5 ingredients until blended; stir in onions. Pour 1-1/2 cups marinade into a large shallow dish. Add chicken and turn to coat. Cover; refrigerate overnight. Cover and refrigerate remaining marinade.
Prepare grill for indirect heat. Drain chicken, discarding marinade in dish. Place chicken on grill rack, skin side up. Grill, covered, over indirect medium heat 15 minutes. Turn; grill until a thermometer reads 170°-175°, 15-20 minutes longer, basting occasionally with reserved marinade.