Combine the chicken, onion, carrots, & celery in a large pot. Season to taste.
Add the chicken broth plus water (if needed) to cover. Bring to a boil, reduce heat, and simmer covered for 45-60 minutes or until the chicken is tender. While the broth is simmering, prepare the dumplings (recipe below).
Remove chicken & vegetables from broth. Discard the skin & bones & chop the remaining chicken; set aside.
Ever so gently, add the dumplings to the broth. Simmer about 20 minutes, or until tender.
Stir the chicken into the broth. You can add the vegetables from earlier back into the broth at this time too, if desired. I usually opt to not add the vegetables back into mine - personal preference. Cook for an additional 10 minutes on low. Serve.