Preheat the oven to 450 degrees F and line two baking sheets with parchment paper.
In a large bowl, whisk together the flour, baking powder, baking soda, sugar and salt. Then add the chives, cheddar and buttermilk, and stir it all together until a dough begins to form. Slowly pour in the melted butter; stir until everything is just combined and moistened.
With a 1/4 cup measuring cup, drop the dough onto the baking sheets, spaced 2 inches apart.
Bake for 12 to 15 minutes, rotating the baking sheets halfway through. Remove from the oven and let cool slightly before serving.