Lightly dust chicken breasts with flour and a little salt and pepper.
In a large skillet, lightly brown chicken breasts to a nice golden brown in olive oil. Once browned on both sides, add mushrooms and champagne. Cook over medium heat, champagne should boil a little, for approximately 1/2 hour. When chicken is tender, transfer chicken to a platter.
Pour cream into skillet. Simmer about 5 minutes, until slightly thickened. Pour sauce over chicken breasts. Serve.