- Place chicken, carrots, celery, and onion in a large soup pot; add enough cold water to cover. Bring to a boil over medium heat; reduce heat to low and simmer, uncovered, until meat falls off of the bone, about 90 minutes. Skim off foam every so often, as needed.
- Remove chicken from the pot and let sit until cool enough to handle; chop meat into pieces, and discard skin and bones.
- Strain out vegetables, reserving the stock; rinse the soup pot and return the stock to the pot. Chop vegetables into smaller pieces; return chopped chicken and vegetables to the pot.
- Warm soup until heated through; season with salt, pepper, and chicken bouillon to taste.