Place chicken in a resealable plastic bag set in a shallow dish. For marinade combine margarita mix, cumin, and lime peel. Pour over chicken; seal bag. Marinate in the refrigerator for 2 to 8 hours. Drain chicken, discarding marinade
For a charcoal grill, grill chicken on the rack of an uncovered grill directly over medium coals for 12 to 15 minutes or until chicken is no longer pink (170 degrees F), turning once halfway through grilling. (For a gas grill, preheat grill. Reduced heat to medium. Place chicken on grill rack over heat. Cover and grill as above.) Remove chicken from grill; cool slightly.
In a small bowl combine mayonnaise, lime juice, and cayenne. Arrange tomatoes, avocados, and red onion on 4 salad plates. Coarsely chop chicken. Add to salads. Drizzle with mayonnaise mixture and sprinkle with black pepper. Makes 4 servings.