1. Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour and butter in a food processor; pulse to blend. Add cheese, chives, salt, and pepper; pulse until mixture resembles coarse meal. Drizzle water into flour mixture until dough forms a ball. Roll dough into a 16 x 8-inch rectangle. Wrap dough in plastic wrap; refrigerate 4 hours or until firm.
2. Preheat oven to 350°.
3. Cut dough crosswise into 64 (1/4-inch-wide) slices. Place 1/2 inch apart on a baking sheet lined with parchment paper. Bake at 350° for 10 minutes or until the edges are lightly browned. Cool straws completely on wire racks.