Preheat oven to 350 degrees. Scoop about 1 tablespoon worth of avocado out of each half; discard or reserve for another use.
Place hallowed avocados in a baking dish, then crack eggs into a bowl, one at a time. Using a spoon, transfer one yolk 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, 20 to 25 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 before serving.