In a large skillet, heat the olive oil over medium heat. Add the sliced onions and cook, stirring occasionally, for about 10-15 minutes until they are caramelized and golden brown.
Add the minced garlic, thyme, salt, and pepper to the skillet. Stir and cook for an additional 1-2 minutes until fragrant.
Push the onions to the side of the skillet and add the chicken breasts. Sear the chicken for about 4-5 minutes on each side until browned.
Pour in the beef broth and Worcestershire sauce. Bring to a simmer, then cover and cook for 15-20 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F.
Remove the chicken from the skillet and slice it. Return the sliced chicken to the skillet, mixing it with the onions and broth.
Sprinkle the shredded Swiss cheese over the chicken and onions. Cover the skillet for 2-3 minutes until the cheese is melted.
To serve, place a scoop of cooked rice in a bowl, top with the French onion chicken mixture, and garnish with chopped parsley.