In blender container, combine all marinade and sauce ingredients; blend until pureed. Place 1/2 cup mixture in 1-quart resealable food storage plastic bag; reserve remaining mixture in small saucepan for sauce. Add chicken breast halves to bag; seal bag and turn chicken to coat. Refrigerate 30 to 60 minutes to marinate, turning once.
Heat grill. When ready to grill, remove chicken from marinade; reserve marinade. Place chicken and onion slices on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Brush onion slices with reserved marinade. Cook 10 to 15 minutes or until chicken is fork-tender and juices run clear, turning once. Discard any remaining marinade.
Meanwhile, heat reserved sauce in saucepan over low heat for 3 to 4 minutes, stirring occasionally. Serve sauce with chicken and onion slices.