Place one chicken, cut into pieces, in 6 quart pot. Salt and pepper to taste. Add enough water to stand at least two inches above the chicken. Cook until it will come off the bone. Remove from broth; remove the bone and skin. Cover and set aside.
Use 1 1/2 cups of almost boiling water. Add self rising flour to this until you have a real stiff batter. Cover and set aside for 2 or 3 hours before using, but stir 2 or 3 times during this time.
When you start to roll it out, pinch off about enough at the time to make 2 medium sized biscuits. Roll as thin as possible. Turn over and roll from the other side. Cut into strips and drop into boiling broth. Repeat this until you have all the dumplings you desire. After dumplings are done, return the chicken and carefully stir in with the dumplings.