PREHEAT oven to 350ºF. Beat peanut butter, dressing, ginger and water in medium bowl with wire whisk until well blended; set aside. Mix cabbages and carrots in large bowl. Add 1/4 cup of the peanut butter mixture; toss to coat. Cover and refrigerate 1 hour.
PLACE chicken in single layer in shallow baking pan; brush with remaining peanut butter mixture. Bake 20 min. or until chicken is cooked through (170ºF). Cut into strips.
SPOON cabbage mixture onto serving platter; top with the chicken and onions.