Place the chicken, carrots, celery and onion in a large soup pot; cover with cold water. Heat and simmer, uncovered, until the chicken meat falls off of the bones (skim off foam every so often).
Take everything out of the pot and strain the stock. Pick the meat off of the bones and chop or shred. Chop the carrots, celery and onion. Season with salt and pepper to taste. Return the chicken, carrots, celery and onion to the pot, pouring back the stock. Reheat and and serve.