Pat the chicken breasts dry with paper towels. Season both sides with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken breasts to the skillet and cook for 5-6 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 heat to medium and add the butter to the same skillet.
Once the butter is melted, add the sliced mushrooms and cook for 5 minutes, stirring occasionally, until they release their moisture and start to brown.
Add the minced garlic and cook for 1 minute until fragrant.
Pour in the chicken broth and bring to a simmer, scraping up any browned bits from the bottom of the skillet.
Stir in the heavy cream and fresh thyme leaves. Simmer the sauce for 3-4 minutes until it thickens slightly.
Return the chicken breasts to the skillet and spoon the mushroom sauce over them. Cook for an additional 2 minutes to warm the chicken.
Remove from heat and serve the chicken breasts topped with the mushroom sauce.