Heat the oven to 300 F.
Cut chicken breasts into 1-inch pieces. In a nonstick frying pan, combine the chicken, celery, onions and tarragon with 1 cup of the unsalted chicken broth. Cook on medium heat until the chicken and vegetables are tender, about 10 minutes. Set aside to cool.
In a baking dish, stir together the rice, wine and remaining 1 cup chicken broth. Let soak for 30 minutes.
Add the chicken and vegetables to the baking dish. Cover and bake for 60 minutes. Check periodically and add more broth if the rice is too dry. Serve immediately.