Combine chicken with flour, 1 teaspoon salt and tarragon in medium bowl; mix well. Heat butter and oil in 5-quart saucepan over medium-high heat. Add chicken and cook until well browned on all sides, stirring frequently.
Add chicken broth, wine, TABASCO® Sauce, carrots, mushrooms and 1/2 teaspoon salt. Heat to boiling over high heat. Reduce heat to low; cover and simmer 20 to 30 minutes or until chicken and vegetables are tender, stirring occasionally.
Serve stew with cooked egg noodles.
Makes 6 servings.