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In a large skillet, in 4 tablespoons hot butter over medium heat, brown chicken breasts on both sides.
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Set chicken aside.
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Add remaining 2 tablespoons butter to drippings in skillet.
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Add sliced mushrooms and cook for about 5 minutes, until golden.
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Remove mushrooms with a slotted spoon and set aside.
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Stir flour, salt and pepper into skillet drippings.
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Pour chicken broth and half-and-half gradually into skillet, stirring constantly, and cook until mixture is thickened.
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Return chicken and mushrooms to skillet with sauce.
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Reduce heat to low, cover, and simmer 25 to 30 minutes, until breasts are cooked through and tender.
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Remove chicken breasts and cut into bite sized pieces and return to skillet.
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Stir and enjoy over a bed of white rice.