Cut chicken into 1-inch pieces and place in a Dutch oven or large saucepan with chicken broth, water, potatoes, carrots, onions, celery, salt and pepper.Cover and cook 45 minutes or until chicken and vegetables are tender.
In a medium bowl, combine flour, corn meal, baking powder and salt.
In a small bowl, beat egg and milk.Add this mixture and melted butter to dry ingredients. Mix only until combined.
Using a tablespoon, gently drop dough onto the stew.
Cover pan tightly, bring to a boil; reduce heat to medium and cook 10-15 minutes.
Notes: After placing dumplings in stew, do not lift cover during cooking; the heat and steam are necessary for the dumplings to cook properly.