Boil hen or fryer in a covered soup pot. Salt to taste. Remove chicken and allow to cool, reserving water. Pull meat from bone.
In a separate pan, saute onion and celery in a few tablespoons of reserved chicken broth. Place chicken shards back into broth, along with onion and celery, and add cream of mushroom soup, tomatoes, and olives.
Cook spaghetti. Layer in a three-quart baking dish, alternating between spaghetti and sauce.
Bake at 350 degrees for 45 minutes. Add grated cheese on top during last 10 minutes.