Season chicken breasts* with salt and pepper. Spread flour out onto a plate or shallow bowl. Dip chicken breasts into flour to coat and shake off excess flour. Set aside.
Heat 2 teaspoons olive oil in a large skillet over medium-high heat. Add in chicken breasts and sear on each side until golden brown and cooked through, about 7 minutes per side. Remove from skillet and set aside while you make sauce. Keep warm.
In the skillet used to make the chicken, heat another 2 teaspoons olive oil over medium-high heat. Add in mushrooms and saute until soft, about 3 to 4 minutes. Add in garlic and cook 1 minute more. Pour in marsala wine and chicken broth Bring to a simmer and cook until liquid is reduced by half, about 6 to 7 minutes.
Reduce heat to low and add chicken back to the pan. Spoon some sauce and mushrooms over the top of the chicken breasts.
Serve chicken warm topped with mushroom marsala sauce. Chicken Marsala is often served over cooked spaghetti pasta.
*This recipe uses four thin chicken breasts. If your chicken breasts are large and thick, you can slice them in half lengthwise, turning two large chicken breasts into four.