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Place chicken in a large heavy zipper bag & pound until its 1/4 inch thick.
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When all breasts are pounded thin, place a layer of prosciutto followed by some shredded cheese over each one, and roll each breast up. Fasten w/ toothpicks.
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Melt the butter w/ the olive oil over medium heat.
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Add the chicken rolls & saute, turning occasionally until golden all over.
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Add the wine to the skillet, turn the burner to low, cover the skillet & simmer for 15 minutes.
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Remove the rolls to a serving plate & cover to keep warm.
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Turn the burner up to high & boil the liquid in the skillet hard for 5 minutes, to reduce. Spoon over rolls & serve.