1. Cook bacon until crisp. I prefer to use an indoor grill. Bacon can also be cooked in a skillet over medium-high heat, or the microwave at about 1 minute per slice. Drain on paper towels, and set aside.
2. Preheat the oven to 350 degrees F (175 degrees C). In a medium bowl, stir together the spinach and blue cheese. Crumble in the bacon, and stir to distribute.
3. Lay the chicken breast halves out on a clean surface, and distribute the spinach mixture evenly onto the centers of them. Fold the chicken over the filling, and secure with toothpicks. Stir together the flour, salt and pepper on a dinner plate. Roll the chicken in the flour to coat.
4. Heat the oil in a skillet over medium-high heat. Quickly brown each piece of chicken on top and bottom. Remove to a lightly greased baking dish, and cover with a lid or aluminum foil.
5. Bake for 30 minutes in the preheated oven, until chicken juices run clear, and filling is hot.