Mix mayonnaise, barbecue sauce, blue cheese, hot-pepper sauce and milk in small bowl.
Place chicken in glass dish. Add 1/3 cup dressing and hot-pepper sauce; turn to coat. Cover; refrigerate 30 minutes.
Meanwhile, mix together carrot, romaine, iceberg and celery in bowl.
Heat broiler. Transfer chicken to broiler pan; discard marinade. Broil 4 inches from heat for 8 minutes; turn and broil 6 minutes or until internal temperature registers 170°F on instant-read thermometer.
Add remaining dressing to greens in bowl. Cut chicken into thin slices. Place on salad. Sprinkle with cheese.