Preheat oven to 375 degrees.
In a large bowl, whisk together the flour, sugar, baking powder and salt. Cut the butter into the flour with a pastry cutter or food processor.
Whisk two eggs and combine with the buttermilk. Add this to the flour mixture and stir until just moist.
Stir in the cheddar, and chives and mix lightly. The dough will be sticky.
Turn the sticky dough out onto a well-floured board, and knead lightly. Cut dough in half. Roll each half into a circle (approximately ¾ inch thick). Cut each circle into 4 wedges. Place on a greased baking sheet.
Whisk remaining egg in a small dish and brush on top of the scones. Let the scones rest for up to 10 minutes before baking (the scones become fluffier when baking with this step).
Bake for 20-22 minutes or until golden.