Place chicken parts in a large pot and cover with water.

Bring to a boil, then reduce heat and simmer until chicken is cooked through (about 1 hour).

Remove chicken from the pot and let it cool slightly.

Debone the chicken and cut the meat into small, bite-sized pieces.

Return the chicken pieces to the broth in the pot.

Peel and quarter the potatoes.

Slice the celery.

Chop the onions.

Add the potatoes, celery, onions, salt, pepper, and egg noodles to the pot with the chicken broth.

Bring the mixture to a simmer and cook until the potatoes and noodles are tender (about 20 minutes).

In a small bowl, mix together the flour or cornstarch and milk until smooth.

Pour the flour/cornstarch mixture into the pot, stirring constantly to prevent lumps.

Continue to cook until the broth thickens slightly (about 5 minutes).

Serve hot.