Cut chicken into portions, place in a saucepan with celery leaves, bay leaf, peppercorns, the one teaspoon salt and the water. Bring to a boil, cover and simmer over low heat for about one hour, or until chicken is tender. Strain, then return broth to saucepan. Cut chicken into small pieces, add to broth with celery and parsley, then simmer.
To make the butter balls, cream butter, add eggs and beat. Gradually add flour and the quarter tsp salt. Beat hard until whole is like a very soft batter. Drop by quarter or half teaspoonfuls into broth, cover and let stand 5 minutes over low heat.