Add chicken to an 8-quart or larger stock pot. Add celery, onion, carrot, bay leaf, parsley, peppercorns, and salt. Cover the ingredients with about 3.5 quarts (14 cups) cold water. Bring to a simmer, then reduce heat to medium low and cook, uncovered, for about 2 hours. Skim off foam that rises to the surface.

Remove chicken pieces to a large bowl and set aside until cool enough to handle and remove the meat from the bones.