MIX lime juice and chili powder; pour over chicken in shallow dish. Cover; refrigerate 20 min. to marinate. Remove chicken from marinade; discard marinade.
PREHEAT barbecue to medium heat. Grill chicken and peppers 5 min. on each side or until chicken is cooked through (170ºF) and peppers are tender.
CUT chicken diagonally into thin strips; set aside. Cut peppers into thin slices; place in large bowl. Add lettuce and onions; mix lightly. Divide evenly among four salad plates; top with chicken. Sprinkle each salad with 2 Tbsp. cheese. Serve with dressing.