Cream the butter and cheese together until well blended.
Stir in the flour and chives and mix with a fork until well combined.
Roll the dough into a ball and wrap in cling film.
Chill in the refrigerator for at least 1 hour.
Roll out to a 5 mm (1/4 inch) thickness and cut into 3.5 cm (1 1/2 inch) rounds with a plain cutter.
Place well apart on greased baking sheets and bake in a preheated hot oven, 220°C (425°F), Gas Mark 7, for 10 minutes.
Cool on a wire rack.
Serve on their own or with dips, or use as a base for savoury spreads.