PLACE large sheet of heavy-duty foil over half of barbecue grate; heat barbecue to medium heat. Meanwhile, place chicken in resealable plastic bag. Add 2 Tbsp. dressing; seal bag. Turn bag over several times to evenly coat chicken with dressing. Refrigerate 10 min. Remove chicken from bag discard bag and dressing.
GRILL chicken on uncovered side of barbecue 6 min. Meanwhile, combine remaining dressing, tomatoes, cheese and basil.
TURN chicken over; place, cooked-side up, on foil on barbecue. Top with tomato mixture. Close lid. Grill 8 min. or until chicken is done (170ºF).