Combine the first 3 ingredients in a large dish. Add chicken, tossing to coat. Cover and marinate in refrigerator 30 minutes to 1 hour.
Cut carrot and celery lengthwise into 12 thin strips using a vegetable peeler. Place strips in a bowl of ice water. Let stand 30 minutes.
Place potato in a saucepan; cover with water. Bring to a boil; cook 15 minutes or until tender. Drain; cool.
Prepare grill. Remove chicken from dish; discard marinade. Place chicken on grill rack coated with cooking spray; grill 5 minutes on each side or until chicken is done. Cut chicken diagonally across grain into thin slices. Set aside.
Arrange lettuce on a large platter. Top with potato, carrot and celery strips, chicken, and tomato halves. Serve with Blue Cheese-Buttermilk Dressing.