In 8-quart Dutch oven or large sauce pot over high heat, heat chicken, onion, water, carrots, pepper and 1 tablespoon salt to boiling. Reduce heat to low; cover and simmer 45 minutes, or until chicken is fork-tender. Remove chicken to cutting board; allow to cool. Meanwhile, prepare the rivels: In medium bowl with fork, stir flour, egg, 1/2 teaspoon salt and approximately 1 tablespoon milk to make a crumbly but moist mixture. With spoon, sprinkle rivels into simmering soup. Add celery; cook 20 minutes, or until tender. Cut chicken meat from bones into small chunks; stir into soup and reheat. This is very good and easy!