Preheat oven to 400 degrees. In a food processor, combine flour, baking powder, salt, and butter. Pulse mixture until pea-size pieces form. Through the feeding tube, add chives and milk; pulse just until combined.
Transfer mixture to a floured surface; with floured hands, pat to a 3/4-inch thickness. Using a 2 1/2-inch round cutter, cut dough into 16 rounds, dipping cutter in flour to prevent sticking. Sprinkle tops lightly with flour.
Place biscuits on a baking sheet, 1 inch apart; bake until golden, about 15 minutes. Serve warm.
To Freeze: After completing step 2, place biscuits on a plate; freeze 2 hours or until firm. Transfer to resealable plastic bags; freeze up to 1 month. To bake from frozen: Preheat oven to 400 degrees. Place biscuits on a baking sheet, 1 inch apart, and bake until golden, 15 to 20 minutes.