Place the onion, carrots, celery, and chicken, in a large soup pot.
Add enough cold water in the pot to cover the chicken and vegetables.
Over medium-high heat, bring the pot to a boil. Once it boils, reduce the heat to medium-low and let it simmer while uncovered until the chicken meat is cooked and the meat falls off the bones. Make sure you occasionally skim off the foam.
Transfer the chicken and vegetables to a large bowl. Using a colander, strain the broth then discard the residue.
Pick the meat off of the bones and shred any large pieces. Chop the carrots, celery and onion.
Return the chicken, carrots, celery and onion to the pot. If desired, season the broth with salt, pepper and chicken bouillon for flavor.
Stir everything well, and serve the chicken soup while it’s hot.