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 from plate into sauce.
Right before serving, drizzle cream sauce over chicken.
