Preheat oven to 350°F. Fit an 8" x 4" loaf pan with parchment paper or spray liberally with cooking spray. Set aside.
In a large mixing bowl, stir together the flour, baking powder, salt, chives and cheddar cheese. Add in the warmed honey and beer. Stir until well-combined, but don't overmix. Some lumps are fine.
Pour mixture into the prepared loaf pan, and bake in preheated oven for about 45 minutes, or until the top is golden brown and the middle is solid. With 10 minutes left in baking, remove the bread from the oven, and drizzle the melted butter on top.