Combine the flour, baking powder, salt, and sugar in the bowl of a stand mixer fitted with the paddle attachment. Add the butter, and mix on low speed until the butter is the size of peas.
With the mixer on low, add the milk, and beat until just mixed.
Add the chives, and mix until just combined.
Dump the dough out on a well-floured board, and knead lightly into a rectangle 3/4-inch thick. Cut out rounds with a 2-and-a-1/2-inch round cutter, and place on a sheet pan lined with parchment paper.
In a small bowl, beat one egg well, and add 1 tablespoon of water. Brush the tops of the biscuits with the egg wash.
Bake for about 20 to 22 minutes, or until the tops are golden-brown and the insides are flaky, yet firm. Serve warm.