Season both sides of the chicken breasts with salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side until golden brown and cooked through. Remove chicken from skillet and set aside.
Reduce heat to medium and add the butter to the same skillet.
Add the sliced onions and cook, stirring frequently, for about 15 minutes until caramelized and golden brown.
Add the minced garlic and dried thyme to the onions and cook for 1 minute until fragrant.
Pour in the white wine to deglaze the pan, scraping up any browned bits from the bottom. Cook for 2-3 minutes until the wine reduces by half.
Add the beef broth and Worcestershire sauce, stir to combine, and simmer for 5 minutes until the sauce slightly thickens.
Return the chicken breasts to the skillet, spoon some of the onion sauce over each piece.
Place a slice of Swiss cheese on top of each chicken breast, cover the skillet with a lid, and cook for 3-4 minutes until the cheese melts.
Remove from heat and serve the chicken topped with the caramelized onion sauce.