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Season chicken breasts with salt & pepper, to taste.
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Heat a large skillet over medium heat then add oil & butter.
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Add chicken & brown on one side, about 8 minutes, then turn over, reduce the heat & cook, covered, at least 10 minutes. Then remove breasts to a serving platter, & keep warm.
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To the skillet add the chopped onion & cook until transluscent, about 5 minutes, then add the wine vinegar & turn heat to medium-low.
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In a small container mix cornstarch with the tablespoon of water & mix thoroughly before adding it to the skillet, stirring to combine. Continue cooking & stirring until slightly thickened, then pour the onion mixture over the chicken breasts & serve.