In a small bowl, whisk the first five ingredients until blended; stir in onions. Pour 1-1/2 cups marinade into a large resealable plastic bag. Add chicken; seal bag and turn to coat. Refrigerate overnight. Cover and refrigerate remaining marinade.
Prepare grill for indirect heat. Drain chicken, discarding marinade in bag. Place chicken on grill rack, skin side up. Grill, covered, over indirect medium heat 15 minutes. Turn; grill 15-20 minutes longer or until a thermometer reads 170°-175°, basting occasionally with reserved marinade.
1 chicken drumstick and thigh: 528 calories, 39 g fat (8 g saturated fat), 129 mg cholesterol, 318 mg sodium, 6 g carbohydrate (3 g sugars, 1 g fiber), 38 g protein.