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Sprinkle chicken breasts with salt and pepper.
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Melt butter in heavy large skillet over medium-high heat.
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Add chicken breasts and sauté until cooked through, about 5 minutes per side.
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Transfer chicken to platter.
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Tent with aluminum foil to keep warm.
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Add shallots to same skillet and sauté 1 minute.
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Add vermouth and mustard and bring to simmer.
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Add cream and 1 1/2 tablespoons tarragon.
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Simmer until slightly thickened, stirring often, about 3 minutes.
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Return chicken and any accumulated juices to skillet.
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Simmer until chicken is heated through, about 1 minute.
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Transfer chicken and sauce to platter.
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Sprinkle with remaining 1 tablespoon tarragon and serve.