BRING dressing just to boil in small saucepan. Add sugar and salt; cook 5 min. or until dissolved. Pour water into 2-gal. stockpot or large bowl. Stir in dressing mixture and pepper. Add chicken. Refrigerate 4 hours.
HEAT grill for indirect grilling: Light one side of grill, leaving other side unlit. Close lid; heat grill to 350ºF. Remove chicken from brine; discard brine. Rinse chicken thoroughly. Place chicken, top side down, on cutting board. Use kitchen shears to cut along one side of the backbone, then cut along the other side to remove bone. Open chicken; place, top side down, on board. Pound to even thickness.
MIX remaining ingredients until blended.
PLACE chicken on grate over unlit area; cover. Grill 40 to 50 min. or until done (165ºF), monitoring for consistent temperature and turning chicken after 20 min. and brushing with the barbecue sauce mixture for the last 15 min.