Pound chicken breasts to an even thickness (about 1/2 inch) between two pieces of plastic wrap. In a shallow dish, combine flour, salt, and pepper, then dredge the chicken in the mixture, shaking off any excess.

Heat olive oil in a large skillet over medium-high heat. Add chicken and cook for 3-5 minutes per side until golden brown and cooked through; remove chicken and set aside.

In the same skillet, add mushrooms and cook until softened, about 5-7 minutes. Stir in garlic and cook for another minute until fragrant.

Pour in Marsala wine and chicken broth, bringing the mixture to a simmer while scraping up any browned bits from the bottom of the skillet. Continue to simmer until the sauce slightly reduces.

Return chicken to the skillet, stir in butter until melted, and coat chicken thoroughly with the sauce. Garnish with fresh parsley before serving.