Heat a large skillet over medium heat. Add the olive oil and butter if using. Let it warm up.
Add the chicken to the pan in a single layer. Don’t move it right away. Let it brown on one side until it releases easily, then flip and brown the other side.
Remove the chicken from the pan and set it aside. It will not be cooked through yet. That’s fine.
Add the mushrooms to the same pan. If the pan looks dry, add a little more oil. Let the mushrooms cook without stirring at first. They will release liquid, then start to brown.
Add the garlic to the mushrooms and stir for about 30 seconds, just until fragrant.
Pour in the chicken broth and scrape the bottom of the pan to loosen any browned bits. Let it simmer for a few minutes.
Stir in the cream or dairy free alternative. Keep the heat low and let the sauce gently come together.
Return the chicken and any juices back to the pan. Simmer until the chicken is cooked through and the sauce thickens slightly.
Season with salt, pepper, and thyme if using. Taste and adjust. Turn off the heat and let it sit for a minute before serving.