Melt the butter in a large nonstick skillet over medium heat. Add the thinly sliced onions and a pinch of salt.
Cook the onions slowly over medium-low heat, stirring occasionally to prevent sticking and ensure even cooking. This process should take about 25-30 minutes. If the onions become too dry add some beef broth to the pan.
Near the end of the cooking time add the balsamic vinegar, Worcestershire sauce, and thyme. Stir well to combine the ingredients and let them cook for an additional 2-3 minutes.
Preheat the oven to 400 degrees F.
Season the chicken breasts on both sides with garlic powder, salt, and pepper. Add the chicken breasts to a baking pan and top them with the caramelized onions. Place one slice of cheese over each chicken breast.
Bake for 25 minutes or until the chicken reaches an internal temperature of 165 degrees F.
Once the chicken is cooked place it under the broiler for 1 minute or until the cheese is golden.