Preheat the oven to 375°F (190°C).
Season both sides of the chicken breasts with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Heat olive oil in a large oven-safe skillet over medium heat.
Add the sliced onions and cook, stirring occasionally, until caramelized and golden brown, about 20 minutes.
Add the minced garlic and dried thyme to the onions and cook for an additional 1 minute until fragrant.
Remove the onions from the skillet and set aside.
In the same skillet, add the chicken breasts and sear for 3-4 minutes on each side until golden brown but not fully cooked.
Return the caramelized onions to the skillet, spreading them evenly over and around the chicken breasts.
Pour the beef broth and balsamic vinegar into the skillet around the chicken.
Transfer the skillet to the preheated oven and bake for 15 minutes.
Remove the skillet from the oven and place one slice of reduced-fat Swiss cheese on each chicken breast.
Return the skillet to the oven and bake for an additional 5 minutes, or until the cheese is melted and the chicken reaches an internal temperature of 165°F (74°C).
Remove from the oven and garnish with chopped fresh parsley before serving.