Sprinkle chicken breasts with salt and pepper. In a large skillet, heat oil over medium-high heat. Add chicken; saute until cooked through, 10 to 12 minutes, turning once. Transfer to a plate; keep warm.
Pour wine into hot skillet; cook, stirring, until reduced by half, about 1 minute. Whisk in cream, mustard, and tarragon. Cook, whisking, until thickened, about 2 minutes.
Pour any accumulated chicken juices into sauce. Right before serving, drizzle cream sauce over chicken.
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