Step 1: In a large skillet heat together oil and butter. Sprinkle chicken breasts with salt and pepper and place in skillet. Brown chicken on both sides for a nice golden brown color. Reducing heat to medium cover skillet and cook chicken for about 15 minutes or until chicken juices run clear. Remove chicken and place on plate, cover with aluminum foil, and set aside.
Step 2: Add cream to skillet and stir while scraping brown bits off bottom of the pan. Put mustard and tarragon into cream mixture and cook for 5 minutes until sauce has thickened. Remove chicken in skillet and coat in sauce. Serve chicken and drizzle with remaining sauce.
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