To prepare the dumplings: Mix the flour with the salt and mound together in a mixing bowl. Beginning at the center of the mound, drizzle a small amount of ice water over the flour. Using your fingers, and moving from the center to the sides of the bowl, gradually incorporate about 3/4 cup of ice water. Knead the dough and form it into ball.
Dust a good amount of flour onto a clean work surface. Roll out the dough (it will be firm), working from center to 1/8-inch thick. Let the dough relax for several minutes.
Add the cream of celery soup to the pot with the chicken and simmer gently over medium-low heat.
Cut the dough into 1-inch pieces. Pull a piece in half and drop the halves into the simmering soup. Repeat. Do not stir the chicken once the dumplings have been added. Gently move the pot in a circular motion so the dumplings become submerged and cook evenly. Cook until the dumplings float and are no longer doughy, 3 to 4 minutes.