In a large stock pot or dutch oven, place the chicken, carrots, celery, onion and salt.
Add the water and bring to a boil. Once boiling, reduce heat, cover and simmer for one hour or until chicken reaches 165°.
Remove chicken to a cutting board and let cool. Turn heat back to high to bring broth to a boil again.
To make the dumplings, combine flour, baking soda, and salt in a medium bowl.
Add shortening and blend with your hands until it resembles coarse meal.
Add buttermilk and stir until dry ingredients are moistened .
On a floured work surface, knead the dough and then roll out to 1/4" thickness.
Using a sharp knife, cut the dough into strips and then into squares.
Drop squares of dough into boiling broth one at a time. Once all dumplings are added reduce the heat again and simmer until dough is cooked through, about 15 minutes.
While dumplings are cooking, remove the skin and bones from the chicken. Shred or chop the chicken and add to the pot with the dumplings.
Stir everything together and serve immediately.