Heat olive oil in a large skillet over medium-high heat.
Season the chicken breasts with salt and pepper, then add them to the skillet. Cook until golden brown on both sides and cooked through, about 6-7 minutes per side. Remove from the skillet and set aside.
In the same skillet, add the sliced mushrooms and cook until they are browned and tender.
Add the minced garlic and thyme to the mushrooms and cook for another minute.
Pour in the chicken broth and heavy cream, stirring to combine. Bring the mixture to a simmer and let it thicken slightly.
Return the chicken breasts to the skillet, spooning the sauce over them. Let them simmer in the sauce for a few minutes to absorb the flavors.
Garnish with fresh parsley before serving.