Preheat oven to 400 degrees F. Separate eggs, putting whites in 1 large bowl and yolks in 4 separate small bowls. Beat whites until stiff peaks form. Fold in cheese. Spoon into 4 mounds on parchment-lined baking sheet; make a deep well in center of each. Bake at 400 degrees for 5 minutes.
Remove from oven and carefully spoon 1 yolk to each well; season with pepper. Bake until yolks are just set, 2 to 3 minutes. Sprinkle with additional bacon and chives. Serve immediately.