DRAIN pineapple, reserving juice. Mix reserved juice with soy sauce, ginger, garlic and 1/2 cup barbecue sauce in slow cooker.
TOP with chicken; cover with lid.
COOK on LOW 6 to 8 hours (or on HIGH 5 hours). About 35 min. before serving, mix cornstarch and water. Add to slow cooker with vegetables, pineapple chunks and remaining barbecue sauce; stir. Cook 30 min. or until heated through.
SERVE with rice.