Pound the chicken breasts to an even thickness. Heat the butter or margarine and oil in a 9x13 inch baking dish and add the chicken. Coat the chicken with the butter or margarine mixture and bake in the preheated oven for 10 to 15 minutes or until breasts just cooked (the center should still be slightly pink).
In a medium saucepan over medium heat, warm the soup, cream, sherry, tarragon, Worcestershire sauce, cilantro, garlic powder and mushrooms. Pour sherry cream mixture over the baked chicken, return to oven uncovered and bake for an additional 15 to 20 minutes. Let cool slightly and serve.