Pat the chicken breasts dry with paper towels. Season both sides with salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken breasts to the skillet and cook for 5 to 6 minutes on each side, or until golden brown and cooked through (internal temperature should reach 165°F). Remove the chicken from the skillet and set aside on a plate.
Reduce the heat to medium. Add the minced garlic to the same skillet and sauté for about 30 seconds until fragrant, stirring constantly to avoid burning.
Add the sliced mushrooms to the skillet. Cook, stirring occasionally, for 5 to 7 minutes until the mushrooms are browned and tender.
Pour in the chicken broth and scrape the bottom of the skillet with a wooden spoon to release any browned bits. Let the broth simmer for 2 minutes to reduce slightly.
Stir in the heavy cream and butter. Cook for another 2 to 3 minutes until the sauce thickens slightly.
Return the cooked chicken breasts to the skillet, spooning some sauce and mushrooms over the top. Sprinkle with fresh thyme leaves.
Simmer for 2 minutes to heat the chicken through and meld the flavors.
Serve the garlic mushroom chicken hot, spooning extra sauce over the chicken.