With a sharp knife carefully loosen the skin from the chicken meat and remove the skin. Season with the salt and pepper.
Melt the butter and olive oil in a 8 inch heavy skillet over medium high heat. Add the chicken and brown on both sides.
Sprinkle the flour over the chicken, add the mushrooms and stir in the chicken broth and white wine. Mix the ingredients.
Bring the sauce to a boil, cover and reduce the heat to low and simmer for about 20 minutes, or until the chicken is fully cooked and reaches an internal temperature of at least 165 Degrees F. Remove the chicken and set aside.
In the same skillet add in the cream to the sauce and bring to a simmer. Cook for about a minute until sauce begins to thicken.
Add the chicken back into the sauce a heat for 1-2 minutes.