Preheat oven to 375 degrees F. Line muffin tins with liners or lightly grease.
In a large bowl, combine flour, sugar, baking powder, and salt. Mix in the cheese and chives.
Make a well in the center and add beaten egg, milk, and butter. Stir together until the ingredients are just combined.
Spoon the batter into the prepared muffin tins 3/4 full. Bake in preheated oven until golden and toothpick inserted in center comes out clean, 20-25 min.