Heat oven to 400°F (205°C).
Whisk flour, sugar, baking powder, baking soda, salt, and pepper together in a large mixing bowl.
Add cubed, cold butter to dry ingredients. Using clean hands, work the butter and flour together until the butter is pea-sized and the mixture is crumbly. Mix in cheddar cheese and chives until combined.
Add Greek yogurt, and mix just until the dough comes together (it will still be crumbly).
Transfer the dough to a lightly floured work surface. Pat the dough into a 1 inch (2.5 cm) thick rectangle. Cut the dough into thirds and stack on top of each other. Repeat this process an additional three times.
Pat the dough for the last time into a 1 inch (2.5 cm) thick rectangle, and use a knife or bench scraper to cut 2 inch x 2 inch (5 x 5 cm) square biscuits.
Place biscuits on a light colored baking sheet lined with parchment paper. Bake for 19–24 minutes until golden brown. Transfer biscuits to a wire rack to cool completely.