In a large bowl, whisk together the flour, baking powder, baking soda, and salt until well combined.
In another bowl, mix the buttermilk, egg, and melted butter until smooth.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. Be careful not to overmix; a few lumps are okay.
Fold in the shredded cheddar cheese and chopped chives until evenly distributed.
Heat a non-stick skillet or griddle over medium heat and add a little butter or oil.
Pour about 1/4 cup of batter onto the skillet for each pancake. Cook until bubbles form on the surface, about 2-3 minutes.
Flip the pancakes and cook for an additional 2-3 minutes until golden brown and cooked through.
Repeat with the remaining batter, adding more butter or oil to the skillet as needed.
Serve warm with your favorite toppings, such as sour cream or additional chives.