Using mallet or bottom of cup, pound chicken breasts to ¼" thickness.
In shallow dish or bowl, combine 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. Turn chicken pieces over and add mushrooms. Pour in wine and sherry. Cover skillet; simmer chicken 10 minutes, turning once, until no longer pink and juices run clear.