Combine water, carrots, onion, celery, thyme, rosemary, salt, and black pepper in a large pot; bring to a boil. Reduce heat and simmer until vegetables are tender, about 15 minutes. Add chicken to soup and cook until no longer pink in the center, about 10 minutes.
Drop biscuit pieces into soup and cook until dumplings are cooked through, 10 to 20 minutes.
