In a shallow dish or bowl, mix together the flour, salt, pepper and oregano. Coat chicken pieces in flour mixture.
In a large skillet, melt butter in oil over medium heat. Place chicken in the pan, and lightly brown. Cook mushrooms in butter in separate pan. Keep chicken and mushrooms warm in the oven while you make the sauce. Pour wine, sherry and broth into skillet. Reduce and thicken with arrowroot. Pour over chicken and mushrooms.