Preheat the oven to 350 degrees F (175 degrees C).
Place chicken breasts in a baking dish; season with salt and pepper.
Bake in the preheated oven until chicken is just slightly pink in the center, about 25 minutes. Remove from the oven.
Cook bacon in a large skillet over medium heat, turning occasionally, until most of the fat has rendered, about 5 minutes. Drain on a paper towel-lined plate. Wrap 2 bacon strips around each chicken breast in the baking dish.
Return chicken to the oven and continue baking until bacon is crispy and chicken is no longer pink in the center, about 15 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Sprinkle chicken with Cheddar cheese. Continue baking until cheese is melted, 2 to 5 minutes. Serve with limes.