1. Place chicken, meaty side down, in a large stockpot. Add carrots, onion, celery, bouillon cubes and 8 cups water. Bring to a simmer over medium-high heat. Reduce heat to medium and simmer 30 minutes.
2. Meanwhile, make dough for dumplings. In a large bowl, whisk together flour, chives, 3/4 tsp of the salt and the baking soda. Pour in half-and-half and stir until it begins to hold together. Transfer dough to a lightly floured surface. With a floured rolling pin, roll out into a 10 x 8-inch square.
3. Remove chicken from pot to a cutting board; reduce heat under pot to low. Let chicken stand until cool enough to handle. Remove and discard skin and bones. Cut meat into bite-size pieces and return to pot. Increase heat to mediumhigh and bring soup to a simmer.
4. Cut dumpling dough into 1-inch pieces. Drop into simmering soup along with thawed peas, black pepper and remaining 1/4 tsp salt. Return to a simmer and cook 5 minutes; serve warm.