Combine first 6 ingredients in a large nonstick skillet; bring to a boil over high heat. Arrange chicken in a single layer in pan; cover, reduce heat, and simmer 20 minutes or until chicken is tender. Remove chicken from wine mixture; set aside, and keep warm.
Combine cornstarch and water; add to pan. Bring to a boil; boil, stirring constantly, 1 minute. Return chicken to pan, coating chicken with mushroom mixture. To serve, place chicken over fettuccine and top with sauce. Garnish with fresh tarragon, if desired.