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1
Stir together olive oil, lemon juice, garlic, rosemary, and salt and pepper in a large bowl. Cut each chicken breast into roughly 6-ounce pieces and place in the bowl. Stir together and refrigerate for 15 to 30 minutes.
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2
Remove chicken from marinade and pat dry (discard marinade). Place two sheets of plastic wrap on your work surface, overlapping slightly, to make 1 wide sheet, and brush lightly with olive oil. Place a piece of chicken in the middle of plastic sheet and brush lightly with oil. Cover the chicken with another wide layer of plastic wrap. Working from the center to the outside, pound chicken breast with the flat side of a meat tenderizer until about 1/4 inch thick. (Don't pound too hard or you'll tear the meat. If that happens it won't be the end of the world, you'll just have a few pieces to cook.) Repeat with the remaining chicken breast pieces.
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3
Season the pounded chicken breasts with salt and pepper on one side only. Dredge lightly in the flour (you will not use all of it) and tap the breasts to remove excess.
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4
Turn oven on low Heat a wide, heavy skillet over high heat and add oil. When oil is hot, place one or two pieces of chicken in the pan; don't crowd them. Cook for 1 1/2 minutes, until bottom is browned in spots. Turn over and brown other side, about 1 1/2 minutes. (Do not overcook or the chicken will be dry.) Transfer to the platter or sheet pan and keep warm in the oven. If there is more than a tablespoon of fat in the pan, pour some (but not all) it off into a jar or bowl.
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5
Turn burner heat down to medium-high. Add mushrooms to the pan. Let them sear for about 30 seconds to a minute without moving them, then stir, scraping the bottom of the pan with a wooden spoon to deglaze. When mushrooms have softened slightly and begun to sweat, add wine, thyme or parsley, and salt and pepper to taste. Continue to stir until wine has evaporated and mushrooms are tender, 5 to 10 minutes. Spoon over the chicken, and serve.
