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Gather the ingredients.
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In a large saucepan, 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 just start to soften, about 10 minutes.
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Sprinkle the flour over the vegetables and cook, stirring, until evenly coated and lightly browned, about 3 minutes.
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Add the wild rice to the saucepan 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.
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Add the chicken and simmer, stirring occasionally, until the wild rice is tender, 10 to 15 minutes longer.
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Stir in the cream and season with salt and pepper. Ladle the soup into bowls and serve.