Combine the flour, salt, and pepper in a shallow dish.
Dredge the chicken breasts in the flour mixture, coating them well.
Heat the olive oil and butter in a large skillet over medium heat.
Add the chicken breasts to the skillet and cook for about 3-4 minutes on each side until golden brown.
Remove the chicken from the skillet and set aside.
Add the sliced mushrooms to the skillet and cook until they start to brown, about 5-6 minutes.
Add the minced garlic to the mushrooms and cook for an additional 1 minute until fragrant.
Pour in the Marsala wine and chicken broth, stirring well to combine.
Return the chicken breasts to the skillet, covering them with the mushroom sauce.
Let the chicken simmer for about 10 minutes until fully cooked and the sauce has thickened.