In a large stockpot, saute carrot, celery, onion, and garlic in olive oil for 5 minutes. Add stock and wild rice. Bring to a boil, then reduce heat and simmer for 30 minutes. Add chicken, cover and simmer for another 20 to 25 minutes until the rice is tender.
In a small bowl, combine butter and flour to make a smooth paste. Stir the flour mixture into the soup and cook until soup begins to thicken. Add cream and milk. Let simmer an additional 5 to 10 minutes. Season with salt and pepper.