Combine chicken, 2 quarts water, and 1 teaspoon salt in a large Dutch oven; bring to a boil. Reduce heat, cover, and simmer 2 1/2 hours or until chicken is tender. If necessary, add water to maintain at least 3 cups broth. Remove chicken from broth; cool. Bone chicken, and cut into bite-size pieces. Return chicken pieces to broth, and set aside.
Cut shortening into flour with a pastry blender until mixture resembles coarse meal. Add boiling water, stirring with a fork until dry ingredients are moistened. Turn dough out onto a lightly floured surface; roll to 1/8- inch thickness, and cut into 1/2- x 3-inch strips.
Bring broth to a boil. Drop dumplings into broth. Cover immediately; reduce heat, and simmer 10 minutes. Add salt and pepper to taste. Serve immediately.