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PREHEAT grill to medium-high heat. 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 (170°F), 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.