Season chicken cutlets with salt and pepper. Dredge in flour, shaking off excess.
Heat olive oil in a large skillet over medium-high heat. Add chicken and cook for 3-4 minutes per side, or until golden brown and cooked through. Remove chicken from skillet and set aside.
Add mushrooms to the skillet and cook until softened and browned, about 5-7 minutes. Add garlic and cook for 1 minute more.
Pour in Marsala wine and chicken broth. Bring to a simmer and cook until the sauce has reduced slightly, about 5-7 minutes. Stir in butter until melted.
Return chicken to the skillet and coat with the sauce. Simmer for a few minutes to heat through. Serve immediately.