In a Dutch cook and stir carrot, onion, and celery in hot butter for 5 minutes or until tender. Add broth and wild rice. Bring to boiling; reduce heat. Simmer, covered, for 30 minutes. Add chicken pieces. Simmer, covered, for 20 to 25 minutes more or until wild rice is tender.
In a small bowl combine flour and softened butter to make a smooth paste. Stir flour mixture into the rice mixture. Cook and stir until thickened and bubbly. Cook and stir for 1 minute more. Add half-and-half. Cook and stir over medium heat until heated through. Season to taste with salt and pepper.