In a small saucepan, saute the ham, onion and celery in butter for 5 minutes or until ham is slightly browned and vegetables are tender. Add the broth and potatoes; bring to a boil. Reduce heat; cover and simmer for 15 to 20 minutes or until potatoes are tender.
In a small bowl, combine flour and milk until smooth; stir into the chowder. Add the dill and pepper. Bring to a boil, stirring constantly; cook for 1 minute or until thickened.