Melt butter and oil over medium high heat in frying pan. Add chicken breasts and cook, turning once until lightly browned, about 2-3 minutes a side. Remove and set aside.
Add wine to the pan. Bring to a boil, scraping up brown bits from bottom of pan. Stir in mustard, tarragon, salt. Wisk in cream and boil until mixture thickens slightly, about 3 minutes.
Return chicken to pan; turn in sacue to coat, and simmer 5-10 min until chicken is tender.