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HEAT grill to medium-high heat.
POUR 1/4 cup dressing over chicken in shallow dish; turn to evenly coat both sides of each breast. Refrigerate 10 min. to marinate. Meanwhile, cover 4 large plates with salad greens; top with peppers, blueberries and onions. Gradually whisk remaining dressing into mayo in bowl until blended. Refrigerate salads and mayo mixture until ready to use.
REMOVE chicken from marinade; discard marinade. Grill chicken 6 to 8 min. on each side or until done (165ºF).
CUT chicken into thin slices. Drizzle mayo mixture over salads; top with chicken, nuts and basil.