In a large skillet, heat olive oil over medium-high heat. Season chicken breasts with salt and pepper, then add them to the skillet. Cook for about 5-7 minutes on each side until golden brown and cooked through. Remove chicken from the skillet and set aside.

In the same skillet, add sliced onions and cook over medium heat, stirring occasionally, until they are caramelized and golden brown, about 10-15 minutes. Add minced garlic and cook for an additional minute until fragrant.

Pour in the chicken broth, heavy cream, Worcestershire sauce, and thyme. Stir well to combine and bring the mixture to a simmer.

Add the rice to the skillet, stirring to ensure it is evenly distributed. Place the chicken breasts back into the skillet on top of the rice mixture.

Cover the skillet with a lid, reduce heat to low, and let it simmer for about 20 minutes, or until the rice is tender and has absorbed most of the liquid.

Once cooked, sprinkle the shredded Swiss cheese over the chicken and rice. Cover again and let it sit for 5 minutes until the cheese is melted.

Garnish with chopped parsley before serving.