Cook fat chicken until well done, keeping covered with lots of water for broth. Salt to taste.
Combine 2 cups all purpose flour, 1/2 teaspoon baking powder, and 1/2 teaspoon salt; cut in 3 tablespoons shortening until mixture resembles coarse meal. Add 3/4 cup of water and stir until all ingredients are moistened. Turn dough out onto a well floured surface and knead lightly 4 or 5 times. Roll dough very thin, cut into 1 inch squares, and drop into boiling chicken broth. After all dumplings have been added to broth, cover pot and continue cooking for approximately 15 minutes. Do not remove lid until time is up or dumplings will be heavy.