Sprinkle chicken with salt and pepper.
Heat oil in a cast iron skillet over medium heat; cook the chicken breasts in hot oil until no longer pink in the center and the juices run clear, 13 to 15 minutes.
Remove and keep warm
.Place bacon in large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes.
Drain bacon slices on paper towels; reserve 2 tablespoons drippings.
Cook and stir onion and brown sugar in reserved drippings until onion is golden, about 5 minutes.
Place two bacon strips on each chicken breast half; top with caramelized onions and sprinkle with Colby-Monterey Jack cheese.