In a small bowl, combine the first 10 ingredients. Set aside 3 tablespoons marinade for sauce. Pour remaining marinade into a large resealable plastic bag; add onion and chicken. Seal bag and turn to coat; refrigerate overnight. Cover and refrigerate sauce.
Drain and discard marinade. Thread chicken onto eight metal or soaked wooden skewers.
Grill chicken, covered, on an oiled rack over medium heat or broil 4 in. from the heat for 4-5 minutes on each side or until no longer pink. Brush with reserved sauce before serving.
