1In medium bowl, mix vinegars and water. Stir in dressing mix. Stir in oil. Divide dressing mixture in half.
2Place chicken in shallow glass or plastic dish or heavy-duty resealable plastic food-storage bag. Pour half of the dressing mixture over chicken; turn chicken to coat. Cover dish or seal bag and refrigerate 15 minutes. Cover and refrigerate remaining dressing mixture.
3Heat coals or gas grill for direct heat. Remove chicken from marinade; reserve marinade. Cover and grill chicken over medium heat 15 to 20 minutes, turning and brushing with marinade occasionally, until juice of chicken is clear when center of thickest part is cut (170°F). Discard any remaining marinade.
4Cut chicken into slices. Serve chicken on salad greens with remaining dressing mixture. Top with tomatoes.