Combine chicken, celery, carrots, onion, chicken broth, parsley, chicken bouillon granules, salt and pepper in a large pan or dutch oven; add enough water to cover chicken.
Bring to a boil; reduce heat, cover and simmer for 2 hours or until chicken is done.
Remove chicken and let stand until cool enough to handle.
Remove skin from chicken and tear meat away from bones.
Return meat to soup; discard skin and bones.
Add more salt and pepper to taste, if desired.
Return soup to a simmer.
In a mixing bowl, combine dumpling ingredients and mix well to form a stiff dough.
Drop by tablespoonfuls into simmering soup.
Cover and simmer for 15 to 20 minutes.
Serve immediately.
