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Make a few slashed on the skin of the chicken using a sharp knife. Brush the chicken with the crushed garlic and place in a non-metallic dish.
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Pour the wine and white wine vinegar over the chicken and season with salt and pepper, to taste. Cover and marinate as long as possible, preferably overnight.
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Remove chicken pieces with a slotted spoon, draining well. Reserve the marinade.
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Heat the oil and butter in a skillet. Add the shallots (whole) and saute for 2-3 minutes, or until they begin to soften.
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Add the chicken pieces to the skillet and cook for 3-4 minutes, turning, until browned all over.
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Reduce the heat and add 1/2 of the reserved marinade. Cover and cook for 15-20 minutes, add more marinade when necessary.
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Add the balsamic vinegar and thyme and cook for another 4 minutes.
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Serve with polenta or rice (optional).