Sprinkle chicken with salt and lemon pepper.
Heat oil in a large skillet over medium heat. Cook chicken breasts until no longer pink in the center, about 13 to 15 minutes. Remove and keep warm.
In the same skillet, cook bacon strips over medium-high heat until browned, about 10 minutes. Transfer bacon to a plate; reserve 2 tablespoons of drippings in the skillet.
Add sliced onion and brown sugar to the skillet. Cook, stirring occasionally, until onions are golden, about 5 minutes.
Top each chicken breast with two bacon strips, then caramelized onions, and sprinkle with shredded cheese.
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