Preheat oven to 450° F and line a large baking sheet with parchment paper.
Separate egg whites and egg yolks, placing the egg whites in a large bowl and the yolks in a small bowl.
Season the egg whites with salt and pepper. Using a whisk or a hand mixer, beat the egg whites until stiff peaks form. Gently fold in cheese, bacon, and chives. Create 4 mounds of egg whites on the prepared baking sheet and indent the centers of each to look like nests. Bake until slightly golden, about 3 minutes.
Carefully add an egg yolk to the center of each egg white cloud. Season yolk with salt and pepper. Bake until the yolks are just set, about 3 minutes more.