PREHEAT barbecue to medium-high heat. Cook and stir onions and peppers in hot oil in large skillet on medium heat 5 min. or until tender; cover. Set aside; keep warm.
GRILL chicken 8 min.; turn over. Brush with barbecue sauce. Grill an additional 7 to 9 min. or until chicken is cooked through (170°F), turning occasionally and brushing with the remaining barbecue sauce.
FILL rolls with chicken; sprinkle evenly with cheese, onions and peppers.