Mix margarita mix, lime juice and garlic in resealable heavy-duty plastic food-storage bag. Add chicken; seal bag and turn to coat with marinade. Refrigerate, turning bag occasionally, at least 1 hour but no longer than 24 hours. Remove chicken from marinade; reserve marinade.
Heat coals or gas grill for direct heat. Place chicken, skin sides up, on grill. Brush with marinade; sprinkle with 1/2 teaspoon of the salt. Cover and grill 5 to 6 inches from medium heat 15 minutes; turn chicken. Brush with remaining marinade; sprinkle with remaining 1/2 teaspoon salt. Cover and grill 20 to 40 minutes longer, turning occasionally, until juice of chicken is no longer pink when centers of thickest pieces are cut.