Pound the chicken breasts with a meat mallet between two pieces of plastic wrap until they are about ½ inch thick for even cooking.
Season the flour in a shallow dish with salt and pepper to taste (about ½ teaspoon each). Dredge the chicken breasts in the seasoned flour, shaking off any excess.
In a large pan over medium-high heat, heat the olive oil. Cook the chicken breasts for 4 minutes on each side, or until golden brown and cooked through (internal temperature of 165°F). Place the chicken on a platter and set aside.
In the same pan over medium heat, add the shallots and mushrooms. Cook for approximately 3 minutes, stirring periodically, until the mushrooms are softened and the shallots are translucent.
Add the Marsala wine and chicken stock to the pan with the shallots and mushrooms.
Bring the mixture to a boil, then reduce the heat to low and let it simmer for about 10 minutes, or until the sauce has reduced and thickened.
Stir in the butter and parsley until the butter is melted.
Return the chicken to the pan and ladle the sauce over it. Simmer for 2–3 minutes, or until the chicken is fully warmed through.
Serve the chicken marsala with a spoonful of the sauce on top. Enjoy!