Place a large sheet of heavy-duty foil over half of grill grate; heat grill to medium heat. Meanwhile, place chicken in resealable plastic bag. Add 1/4 cup dressing and seal bag. Turn bag over several times to evenly coat chicken with dressing. Refrigerate 10 minutes (I marinate it all day if I remember in time). Remove chicken from bag; discard bag and dressing.
Grill chicken on uncovered side of grill for about 6 minutes. Meanwhile, combine remaining 1/4 dressing, tomatoes, cheese and basil.
Turn the chicken over and place cooked-side up, on foil on the grill. Top with tomato mixture. Close lid. Grill 8 minutes or until chicken is done.
*Sometimes we add a splash of balsalmic vinegar to give it a bit more zip.
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