Rinse chicken well. Do not remove skin. In a large stock pot, cover chicken completely with water and about one-inch more. Add two stalks of celery with leaves, 2 carrots, and onion. Salt generously. Bring to a boil. Cover, reduce heat and simmer for about 45 minutes.
Remove pot from heat. Discard celery and carrots. Skim fat or grayish foam and discard. Remove chicken from pot. Set aside and cool completely.
Remove cooled chicken from the bone and tear into bit size pieces. Add to the broth along with the remaining carrots and celery. Simmer for about 45 minutes.
While the broth is simmering, cook pasta in a medium saucepan according to package directions. Drain well and add to soup mixture, one cup at a time. Add pepper and adjust salt as needed.