Preheat oven to 425.

Whisk together flour, Cheddar, chives, salt, baking soda, and cayenne pepper in a medium bowl. Using a pastry blender or two knives, cut in the butter.

In a small bowl, stir together the buttermilk and eggs. Stir until flour mixture just until all ingredients are wet.

Drop dough by heaping tablespoonfuls onto a greased cookie sheet. Bake until golden, between 15 and 18 minutes.