HEAT grill to medium-high heat.
BRUSH chicken with 2 Tbsp. dressing. Grill 5 to 6 on each side or until done (165ºF).
TOSS lettuce with carrots, avocados and cucumbers in large bowl. Add remaining dressing; mix lightly. Place on 4 plates.
CUT chicken into thin slices; place on salads. Top with cheese.