Chicken Marsala (with mushrooms not cream)

This simple recipe serves 6

3 whole boneless chicken breasts with skin (about 2 1/2 pounds),
halved
1 1/2 tablespoons olive oil
3 1/2 tablespoons unsalted butter
1 onion, sliced thin
3/4 pound mushrooms, sliced thin
1/2 cup Marsala
1 cup chicken broth

Can add 1/2 & 1/2 if you want something naughtier.