Season the chicken breasts with salt and pepper.
Heat olive oil in a large skillet over medium heat. Add chicken and cook until golden and cooked through, about 6-7 minutes per side. Remove chicken and set aside.
In the same skillet, melt butter. Add garlic and sauté for 1 minute until fragrant.
Add mushrooms and cook until softened and browned, about 5 minutes.
Pour in chicken broth and bring to a simmer, scraping up any browned bits from the pan.
Stir in heavy cream and cook until sauce thickens slightly, about 3-4 minutes.
Return chicken to the skillet and spoon sauce over the top. Cook for another 2 minutes to warm through.
Garnish with fresh parsley before serving.