Whisk together flour, baking powder, and salt in a bowl. Cut in shortening with a knife or pastry blender until the mixture resembles coarse crumbs. Stir Cheddar cheese and chives into flour mixture; gradually stir in milk to form a soft dough.
Turn dough out onto a lightly floured surface and with floured hands, knead until smooth, about 15 times. Roll dough out to a 1-inch thickness with a floured rolling pin. Cut biscuits with a 2 1/2-inch round cookie cutter; place onto an ungreased baking sheet. Press dough trimmings together, roll out again, and cut remaining dough into rounds.
Bake in the preheated oven until golden brown, about 15 minutes.
