Combine in medium bowl: mayonnaise, oil, cumin, pepper sauce, cilantro, lime juice, and lime zest. Reserve 1/2 cup marinade for later use. Place remaining marinade and chicken in zip-top bag (or shallow dish); seal bag and toss to coat. Let stand 10 minutes (or refrigerate overnight) to marinate.
Preheat oven to 450 degrees F. Line baking sheet with foil.
Arrange chicken 2 inches apart on baking sheet and sprinkle with seasoning; bake 10 minutes.
Turn chicken over; bake 10 more minutes or until chicken is 165 degrees F. (For more browning, broil 2-3 minutes.) Brush reserved marinade over chicken. Serve.