In a saucepan cook onion in the butter until tender; blend in flour. Gradually add milk, stirring. Continue cooking, stirring constantly, until mixture thickens. Add cheese and stir until cheese is melted.
Place a layer of egg slices in a 10x6x1 1/2-inch baking dish. Cover with half of the cheese sauce, half of the potato chips, and half of the bacon. Repeat layers. Bake at 350° 15 to 20 minutes, or until heated through.