Preheat oven to 400 degrees F. Lightly grease a baking sheet.
Sift together the flour, baking powder, sugar, salt, and chives. Cut the cold butter into 8 pieces. Using a pastry cutter or a fork cut in the butter.
Mix in the shredded cheese. Combine the egg and milk together and add to the flour mixture. Mix just until the wet ingredients are incorporated.
On a floured surface pat the dough out into an 8-inch circle. Cut into 8 triangles. Place the scones on a prepared pan and bake for 12 to 14 minutes or lightly browned.