In a 2- to 3-quart pan over medium-high heat, melt butter or margarine. Add flour and stir until bubbling. Remove pan from heat and whisk in chicken broth and diced green chilies. Stir over high heat until boiling, 3 to 4 minutes. Add shredded cheddar cheese and stir until melted. Serve hot, or let cool, cover, and chill up to 1 day; if chilled, stir over high heat until steaming.
Nutritional analysis per 1/2 cup.