Season the chicken breasts with salt, pepper, and thyme.
Heat the olive oil in a large skillet over medium heat.
Add the chicken breasts and cook for 5-6 minutes per side, or until browned and cooked through. Remove the chicken from the skillet and set aside.
Add the butter to the same skillet, then add the sliced mushrooms. Cook for 5-7 minutes, stirring occasionally, until the mushrooms are softened and browned.
Add the minced garlic and cook for 1 minute, stirring often.
Pour in the Marsala cooking wine and chicken broth, scraping up any browned bits from the bottom of the pan.
Let the sauce simmer for 5-7 minutes, or until slightly reduced.
Stir in the heavy cream and simmer for another 2-3 minutes, until the sauce is smooth and slightly thickened.
Add the chicken back to the skillet and spoon the sauce over the top.