In a deep skillet, heat oil on high. Coat chicken with flour, add to skillet, reduce heat and cook on low for 10 minutes (or until cooked through). Remove chicken breasts to a platter and keep warm.
To the same skillet, add the shallots, saute for 1 minute, then add wine and heat until reduced by half. Add stock and heat for 5 minutes until sauce thickens.
Meanwhile, in a small pan, saute mushrooms in a little oil. Add tarragon to mushrooms, then add both to the chicken and wine sauce. Cook all for 7 minutes, stir in port and cook for 5 more minutes.
Arrange the chicken on a platter and spoon sauce over it. Garnish with parsley and extra thyme sprigs. Serve.
