How to Make It
Place chicken, celery, and carrots in a Dutch oven; add water and 2 teaspoons of the salt. Bring to a boil over high; cover, reduce heat to medium-low, and simmer until tender, about 1 hour. Remove chicken from broth, and let stand until cool enough to handle, about 15 minutes. Remove and discard skin and bone from chicken, and cut meat into bite-size pieces. Bring broth to a boil over high; stir in pepper.
Meanwhile, combine flour, baking soda, and remaining 1/2 teaspoon salt in a large bowl; cut in shortening with a pastry blender (or use your fingers) until mixture resembles coarse meal. Add buttermilk, stirring with a fork until dry ingredients are moistened. Turn dough out onto a well-floured surface, and knead lightly 4 or 5 times.
Pat dough to 1/2-inch thickness. Pinch off dough in 1 1/2-inch pieces, and drop into boiling broth. Reduce heat to medium-low, and cook, stirring occasionally, until desired consistency is reached, about 8 to 10 minutes. Stir in chicken. Garnish servings with chives.