Remove gizzards from hen and wash hen thoroughly with water. Cut hen into several pieces.

Heat oil in a large pot over medium-high heat. Add hen pieces and cook in hot oil until browned on all sides. Add celery, carrots, onion, garlic, and potatoes; cook and stir until onion is tender.

Pour in chicken broth. Use more or less broth to your taste, but make sure to cover all the ingredients in the pot. Bring to a boil, then reduce heat and simmer until vegetables are tender and hen is cooked through.

Remove hen from the pot and remove meat from the bones. Discard bones and return meat to soup. Serve hot.