STEP ONECOMBINE chicken, onion, carrot, celery and water in Dutch oven. Bring to a boil. Reduce heat to low. Cover and simmer 1 hour or until tender. Remove chicken from broth. Remove vegetables from broth and discard. Cool chicken and broth slightly. Remove chicken from bones. Cut into bite-sized pieces. Skim fat from surface of cooled broth. Bring broth to a boil. Add butter, salt and pepper.
STEP TWOPLACE flour in medium bowl. Cut in shortening with pastry blender or 2 knives until mixture resembles coarse crumbs. Add 1/2 cup chicken broth. Stir with fork until dough leaves sides of bowl.
STEP THREEROLLED DUMPLINGS: Roll out dough on lightly floured surface to 1/8-inch thickness. Cut dough into strips or small squares.
STEP FOURDROP DUMPLINGS: Press dough on lightly floured surface to 1/2-inch thickness. Pinch off dough in small pieces.
STEP FIVEDROP dumplings 1 at a time into boiling broth. Reduce heat to low. Cover and simmer 15 minutes or until dumplings are firm. Gently stir once or twice during cooking to prevent dumplings from sticking together. Stir chicken pieces into dumpling mixture just before serving.