Season chicken with salt and pepper.
Heat olive oil in a large skillet over medium heat and brown the chicken on both sides, about 5 minutes each.
Remove chicken and set aside. Add butter to the skillet and sauté mushrooms until golden.
Stir in garlic and cook for 1 minute.
Pour in chicken broth and let it simmer for 3 minutes.
Add heavy cream and thyme, stir well, and bring to a gentle simmer.
Return chicken to the pan, cover, and cook until chicken is fully cooked through, about 10 minutes.
Garnish with parsley before serving.