Mix mayo and onions; cover. Refrigerate until ready to serve.
Brush chicken with oil.
Grill chicken 4 min. on each side.
Brush lightly with barbecue sauce. Continue grilling 2 min. or until chicken is cooked through (170F), turning and brushing occasionally with the remaining barbecue sauce.
Spread top halves of rolls with the mayo mixture.
Place lettuce and tomato slices on bottom halves of rolls; cover with the chicken and tops of rolls.