Coat chicken breasts with flour and a little salt and pepper. You can use a bag to toss the chicken in the flour.
In a large skillet, lightly brown chicken breasts in olive oil. Once browned on both sides, add mushrooms and champagne. Cook over medium heat, for approximately 35 minutes. Transfer to plate or serving tray.
Pour cream and mayo into skillet. Simmer about 5 minutes, until slightly thickened. Pour sauce over chicken breasts. Serve.