Pound chicken breasts with the flat side of a meat mallet to flatten out and ensure even cooking.
Heat olive oil in a skillet over medium-high heat. Add chicken breasts and season with salt and pepper. Cook until chicken breasts are browned and no longer pink in the middle, 5 to 8 minutes per side. Transfer to serving plates and keep warm.
Add butter, bacon, sage leaves, balsamic vinegar, maple syrup, and chopped hazelnuts to the same skillet. Bring to a quick boil. Reduce heat and simmer, stirring regularly, until sauce thickens slightly, 3 to 4 minutes. Season with salt and pepper. Pour sage sauce over chicken.