Heat olive oil and butter in a large skillet over medium heat. Once melted, add the sliced onions.
Sprinkle the onions with salt and cook, stirring occasionally, for about 15 to 20 minutes, until they are caramelized and golden brown.
While the onions cook, season the chicken breasts with black pepper, garlic powder, and thyme.
Push the caramelized onions to the side of the skillet and add the chicken breasts. Sear the chicken on both sides for about 3-4 minutes until they are browned.
Pour the beef broth into the skillet, bringing everything to a simmer, and cover the skillet. Cook for an additional 10 minutes until the chicken is cooked through and juices run clear.
Preheat your oven broiler. Once the chicken is fully cooked, remove the skillet from heat and sprinkle the cooked onions evenly over the chicken.
Top each chicken breast with shredded Gruyère cheese and place the skillet under the broiler for 2-3 minutes, until the cheese is bubbly and golden.
Serve the French Onion Chicken hot, garnished with fresh thyme if desired.