Prepare rice mix according to package directions, omitting butter. Meanwhile, in a large saucepan, saute the chicken, mushrooms and onions in oil until chicken is no longer pink and vegetables are tender. Add garlic; cook 1 minute longer.
Add the prepared rice, broth, tarragon, thyme and pepper; bring to a boil. Combine cornstarch and evaporated milk until smooth; stir into rice mixture. Return to a boil; cook for 1-2 minutes or until slightly thickened. Garnish with green onions.