Set a nonstick pan on MEDIUM heat. Add the unsalted butter. Once the butter has melted, crack 2 eggs into the hot pan.
Turn the heat to LOW and cook the eggs for 2 minutes or until the egg white begins to set and the egg yolk is still runny.
Flip the eggs with a spatula. Let them cook for an additional 30 seconds. When done, the egg yolk should still be runny in the center.
Remove the eggs from the pan. Place on a plate and season with freshly ground black pepper. Garnish with chopped chives.