Preheat oven to 350°. Place avocados in a baking dish, then crack eggs into a bowl. Using a spoon, transfer yolks to each avocado half, then spoon in as much egg white as you can fit without spilling over.
Season with salt and pepper and bake until whites are set and yolks are no longer runny, about 20 minutes. (Cover with foil if avocados are beginning to brown.)
Meanwhile, in a large skillet over medium heat, cook bacon until crisp, 8 minutes, then transfer to a paper towel-lined plate and chop.
Top avocados with bacon and chives and serve with a spoon.
