Heat grill to medium heat.
Cook onions in boiling water 5 min. or until tender; drain. Place onions in medium bowl. Add vinegar and sugar; mix well. Refrigerate until ready to use.
Grill chicken 5 to 6 min. on each side or until done (165ºF), brushing with barbecue sauce for the last 5 min. Cut into thin strips.
Top tortillas with chicken, onions and Singles; fold in half. Grill 1 to 2 min. on each side or until Singles are melted and quesadillas are lightly browned on both sides. Sprinkle with cilantro.