Preheat the oven to 375°. Melt butter in a medium saucepan over medium heat. Add Cheddar cheese, and cook 2 minutes, stirring constantly. Stir in flour, sour cream, and chives.
Spoon batter into ungreased miniature (1 3/4") muffin pans, filling two-thirds full. Bake at 375° for 20 to 22 minutes. Remove muffins from pans immediately.