Add the Cheddar cheese, fresh chives, and cooked bacon. Using a food processor, pastry cutter, or fingertips incorporate the chilled butter into the dry ingredients until the mixture resembles coarse meal. Whisk the flour, sugar, baking powder, salt, and baking soda in a large mixing bowl. In a heavy-bottomed skillet over medium-high heat, cook the bacon until crisp and brown.
Line a baking sheet with parchment paper.