Heat oven to 425° F.
In a large bowl, combine the flour, sugar, baking powder, and salt. Using a pastry blender or 2 knives held crisscross fashion, cut in the butter until the mixture resembles coarse crumbs. Stir in 2/3 cup of the cream. Add the Cheddar and chives and use your hands to combine; the dough should be crumbly. Knead the dough a couple of times until it comes together. Gently pat it into a ball, then flatten slightly into a 1-inch-thick disk. Transfer to a baking sheet. Slice into quarters, then cut each quarter in half. Brush the top with the remaining cream. Bake for about 30 minutes or until golden.
Tip: For a hearty sandwich, split a scone in half, spread it with mustard, and fill it with leftover turkey or ham.