In a Dutch oven, melt the butter.
Add the celery, carrots, onion, garlic, thyme and a generous pinch each of salt and pepper. Cook over moderate heat, stirring occasionally until the vegetables start to soften, about 8 minutes.
Sprinkle the flour over the vegetables and cook, stirring until evenly coated and lightly browned, about 3 minutes.
Add the wild rice to the Dutch oven and gradually stir in the stock and water. Bring to a boil, then simmer over moderately low heat, stirring occasionally until the vegetables are tender, about 30 minutes.
Add the chicken and mushrooms and simmer another 10-15 minutes until the rice is tender. Keep stirring occasionally.
Stir in the cream and sherry. Check for seasoning, and add a pinch of salt if needed. Simmer 2-3 minutes longer.
Ladle into soup bowls and serve.
Can be refrigerated for up to 2 days.