Step 1: Sprinkle chicken breasts with salt and pepper.
Step 2: Melt butter in heavy large skillet over medium-high heat.
Step 3: Add chicken breasts and saute until cooked through, about 5 minutes per side.
Step 4: Transfer chicken to platter.
Step 5: Tent with aluminum foil to keep warm.
Step 6: Add shallots to same skillet and saute 1 minute. Add vermouth and mustard and bring to simmer. Add cream and 1 1/2 tablespoons tarragon. Simmer until slightly thickened, stirring often, about 3 minutes.
Step 7: Return chicken and any accumulated juices to skillet.
Step 8: Simmer until chicken is heated through, about 1 minute.
Step 9: Transfer chicken and sauce to platter.
Step 10: Sprinkle with remaining 1 tablespoon tarragon and serve.
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