Saute ham, onion, and celery in margarine in a Dutch oven over medium heat until vegetables are tender.
Measure 1/4 cup chicken broth, and set aside. Add remaining broth, half-and-half, beer, and cheese to ham mixture. Cook over medium heat, stirring constantly, until cheese melts.
Combine reserved 1/4 cup broth and flour in a small bowl; stir until smooth. Add flour mixture to mixture in pan, stirring constantly. Cook over medium heat, stirring constantly, until slightly thickened.