Preheat oven to 350 degrees F. Meanwhile, heat the olive oil in an ovenproof skillet (at least 10" diameter) over medium heat, add the bacon, and cook until browned but not crisp. Remove the bacon, add the potatoes to the skillet, cook until tender and browned, remove and set aside with the bacon.
Mix the eggs and milk in a medium bowl, discard any fat that has accumulated in the skillet and add the butter, then turn the heat to low and add the eggs to the hot pan. Distribute the bacon, potatoes, and chives evenly over the eggs, and salt and pepper to taste.
Put the skillet in the oven for approximately 8 minutes, or until the eggs are just set. Remove from the oven, divide in half, and serve.