Prepare the oven and preheat to 200 degrees C or 400 degrees F.
Apply cooking spray in a baking dish.
Put a large skillet on the stove and turn the heat to medium-high.
Add butter and let it melt.
Add the onions, then sauté for a few minutes until soft.
Turn the heat to medium-low, then add the garlic, pepper, and thyme. Sauté until aromatic.
Add the balsamic vinegar and beef broth, then stir until well blended. Make sure to scrape the bottom of the skillet to get the browned bits.
Simmer everything for 10 minutes or until the onions caramelize.
Add 1/3 of the mixture into the prepared baking dish and spread it evenly.
Lay the chicken breasts over the onion layer, then season with salt to taste.
Scatter the rest of the onions over the chicken.