In a medium-sized bowl, whisk together the flour, salt and pepper.
Place the butter in a stand mixer fitted with the paddle attachment, and mix on medium-low speed until creamy.
Slowly add the cheddar cheese, followed by the flour mixture and chives. With the mixer still running, drizzle in the water to help bring the dough together.
Wrap the dough in plastic, flattening into a disc. Chill until firm, at least 30 minutes.
Preheat the oven to 350 degrees F and line a baking sheet with parchment paper.
On a lightly floured surface or between 2 sheets of parchment paper, roll the dough to 1/4 inch thick. Use a 2 1/2 or 3 inch cookie cutter to make small crackers, re-rolling the dough as needed. (An alternative method is to chill the dough in the shape of a log and then slice it). For best results, chill the cut crackers for 15-20 minutes before baking to firm up the butter.
Bake on the prepared sheet pan for approximately 18-22 minutes or until golden brown.