1 at a time, place chicken breasts between 2 sheets of wax paper (or plastic wrap). With a mallet pound chicken breasts until they are about ¼” thick.
On a plate combine flour, salt and pepper, and oregano. Dredge chicken breasts in flour until coated thoroughly.
Heat olive oil and butter in a large skillet. Fry chicken breasts until they are almost fully cooked (about 3 minutes on each side).
Remove from pan and keep warm in the oven at 175 degrees.
Deglaze the pan with marsala wine. Make sure to scrape up all the brown bits on the bottom of the pan and mix them with the wine.
Add chicken broth mushrooms and garlic. Cook on medium-high for 10 minutes or until the sauce has reduced by half.
Add chicken breasts back to the pan and cook for another 10 minutes. The sauce should now have become somewhat thick. Serve on a bed of linguini.