Preheat oven to 425 degrees
Sift together flour, baking powder, baking soda, and salt in a large mixing bowl.
Cut up butter into small cubes.
Add the butter cubes to the flour mixture and blend with a pastry cutter until it resembles the texture of oatmeal.
Add cheddar cheese and chives to the flour and butter mixture. Mix well.
Pour buttermilk in and stir until just mixed.
Gather the dough from the mixing bowl and place it on a lightly floured surface.
Press out the dough and then fold it in half.
Turn the dough, press it out a little again, and fold it in half again.
Turn, press and fold a third time.
Roll the dough into a rectangle about 1 inch thick, and cut out as many biscuits as you can with a 3 inch biscuit cutter.
Place each biscuit on a parchment lined or greased baking sheet.
Gather the remaining dough scraps together and roll it out. Then cut out more biscuits. Repeat until all the dough is used.
Bake the biscuits for 15 minutes or until the tops are golden brown.
Remove from the oven, brush with melted butter and sprinkle a few chopped chives on top.