If you're baking eggs for several people, note that you'll likely need to cook them for a few minutes longer than if you're just baking one or two. Keep an eye on the yolks so they don't get overdone. Note that you'll need individual, 4-ounce ramekins for making these - they're inexpensive and here is one good place to buy them.
Grease the inside of 4, 4-ounce ramekins with butter. Add one tablespoon of half and half or heavy cream into the bottom of each buttered ramekin. Top the cream with one egg and a large pinch of cheese. Season with salt and freshly ground black pepper and sprinkle with chives.
Bake eggs 10 to 12 minutes until the yolk reaches your desired consistency (I recommend removing them while the top is still a bit wobbly to ensure a runny yolk. For firmer yolks, cook up to 15 minutes). Serve.
Feel free to swap in a different cheese for the Gruyere. I've used cheddar, parmesan, and even crumbled feta cheese with good success!