Melt the butter and heat the oil in a frypan over medium-high heat. Season chicken with salt and pepper and place in the frypan. 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 frypan to coat with sauce. Drizzle chicken with remaining sauce to serve.