Combine the flour, salt, pepper, and oregano and mix well.
Heat the oil and butter in a large skillet over medium heat until bubbling lightly.
Dredge the chicken in the flour mixture and shake off the excess.
Cook the chicken for about 2 minutes on the first side, until lightly brown. Flip the breasts and add the mushrooms and onions (if desired) around the chicken. Cook for about 2 more minutes, until the chicken is lightly browned on the second side.
Add the wine, stir the vegetables, cover, and simmer for about 10 minutes, until the chicken is cooked through.