Melt the butter and heat the oil in a skillet over medium-high heat.
Season chicken with salt and pepper, and place in the skillet. Brown on both sides. Reduce heat to medium, cover, and continue cooking 15 minutes, or until chicken juices run clear. Set aside and keep warm.
Stir cream into the pan, scraping up brown bits. Mix in mustard and tarragon. Cook and stir 5 minutes, or until thickened. Return chicken to skillet to coat with sauce. Drizzle chicken with remaining sauce to serve.
Contribution by: FoodandWine.com, recipe By GRACE PARISI
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