PREHEAT barbecue to medium-high heat. Cook and stir onions and peppers in oil in skillet on medium heat until tender; set aside.
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. Top chicken with Singles. Grill an additional min. or until Singles are melted.
FILL rolls with chicken, onions and peppers.