In a skillet over medium-high heat, heat the oil and melt the butter. Season chicken with salt and pepper. Place chicken in the skillet and brown on both sides. Reduce heat to medium, cover, and continue cooking approximately 15 minutes or until chicken juices run clear. Remove chicken and set aside, keep warm.
Stirring cream into the pan, scrap up brown bits left in bottom of the pan. Mix in mustard and tarragon, cook and stir 5 minutes or until thickened. Return chicken to skillet and coat with sauce. Drizzle chicken with remaining sauce to serve.