Season the chicken breasts with salt and pepper on both sides.
In a large skillet, heat the olive oil over medium heat. Once hot, add the chicken breasts and cook for about 6-7 minutes per side until golden brown and cooked through. Remove from the skillet and set aside.
In the same skillet, add the chopped onion and sauté for 2-3 minutes until translucent. Add the minced garlic and sliced mushrooms, cooking for an additional 5 minutes until the mushrooms are tender.
Pour in the chicken broth, scraping the bottom of the skillet to deglaze. Bring it to a simmer.
Lower the heat and stir in the heavy cream, thyme, and additional salt and pepper to taste. Allow the sauce to simmer for another 3-4 minutes until it thickens slightly.
Return the cooked chicken breasts to the skillet, coating them with the creamy mushroom sauce. Let them simmer together for another 2-3 minutes to heat through.
Serve the creamy mushroom chicken hot, garnished with fresh parsley.