Season chicken breasts with salt and pepper.
In a large skillet, heat olive oil over medium-high heat. Cook chicken for 5-6 minutes per side until golden and cooked through. Remove from pan and set aside.
Add butter to the same skillet. Sauté onions for 2-3 minutes until translucent. Add garlic and mushrooms, cooking until softened and browned.
Pour in chicken broth, scraping the bottom of the pan. Stir in heavy cream and thyme. Simmer for 5-7 minutes until sauce thickens.
Return chicken to skillet and coat with sauce. Cook for an additional 2 minutes.
Serve hot, garnished with parsley if desired.