Toss to combine tomatoes, lettuce, 1 tsp. olive oil, vinegar, salt and pepper in a mixing bowl. Set aside.
Heat a large nonstick pan, add the remaining 1 teaspoon olive oil and place 2 ring molds in the pan. Crack the eggs into the molds, reduce the heat to low and cover. Cook over low heat until the whites have cooked through, about 3-4 minutes. Lightly season with salt and pepper and top with chives if desired. You could also use hard boiled eggs in this recipe.
Spread the mayonnaise on each slice of toast and lightly sprinkle with salt and pepper. Divide the bacon, lettuce and tomato between the bread slices. Place an egg on top of each sandwich and serve.