Cut Chicken breasts in half, crosswise.Flatten between plastic wrap or freezer bag, to .5 inch thick.Sesaon with salt and pepper, set aside.
In wide skillet, melt 1 tablespoons butter with 1 tablespoons olive oil over high heat until butter sizzles.Add mushrooms, season with more salt and pepper and cook, sitrrig occasionally, until mushrooms are seared and cooked through (6-8 minutes).Add garlic during last minute o cooking.
Scrape mushrooms/garlic onto a plate, getting all garlic bits out o pan.
Dredge chicken in flour, shaking off excess.Heat 1 tablespoons butter and 1 tablespoons olive oil.Add chicken pieces in a single layer, do not crowd them.Cook in 2 batches if necessary.Sautee, turning over midway through cooking, until they are browned on each side.Remove to a separate plate.
While chicken is cooking, stir corn starch into stock until it’s completely dissolved, then mix with the Marsala.
Into the empty pan, pour about 1/3 of marsala mixture, scraping bottom to get up the browned bits.Add rest of Marsala mixture, chicken and mushrooms.
Cook in the sauce over medium heat, turning chicken over occasionally to baste in the sauce, until the chicken is cooked and sauce is thickened, about 5-6 minutes.Remove from heat and stir in another tabs o butter, balsamic vinegar and chopped parsley.Taste for seasoning, add more salt I necessary.
Serve warm over wide noodles over pasta or mashed potatoes.