Preheat oven to 400°F: Line 2 heavy baking sheets with silpat or parchment paper.
Make the dough: Whisk flour, baking powder, sugar, baking soda, salt and pepper in a large bowl. Using fingertips, rub butter into dry ingredients until coarse meal forms. Stir in the chives. Add cheese and buttermilk; stir with fork just until a sticky dough forms (bits of cheese will be visible in dough).
Knead the dough and form into rounds, cut into wedges: Turn dough out onto a lightly floured surface and knead gently 8 times with floured hands. Do not over-knead! Form into a round, about ¾-inch to an inch thick. Cut the round into 8 wedges.
Use a pastry brush to brush on some extra buttermilk: over the surface of the wedges.
Bake: Arrange wedges about ½ inch apart on an un-greased large baking sheet and bake at 400°F in the middle of the oven until golden brown, about 20 minutes.
Cool on a rack.
Best eaten just baked and warm, with a little butter.
