Preheat oven to 400°F. Whisk together flour, sugar, baking powder, baking soda, and salt in a large bowl.
Grate the cold butter using a cheese grater. This is an easy way to get it into small pieces to incorporate in the dry ingredients. If you do not have a cheese grater, you can just cut into small cubes. Blend the grated butter in with the flour mixture using a pastry cutter or 2 knives. The mixture should be clumpy and look like course crumbs.
Mix in the cheese and chives. Add the buttermilk and mix into the flour mixture until JUST incorporated. DO NOT over mix, this will make the scones too dense.
Put a small amount of flour onto a clean surface and knead the dough briefly. Shape the dough into a circle that is about 1 ½ inches thick. Cut the circle in half and then each half into 4-5 wedges (depending on how big you want your scones).
Put the wedges on a baking sheet covered with parchment paper. Brush the tops with a little bit of buttermilk.
Bake for 20-22 minutes until tops are golden brown and toothpick inserted comes out clean. Cool on a wire rack.
