Melt the butter in a large pot over medium heat until bubbling.

Add the onion, carrot, celery, and garlic. Sauté until the vegetables are softened but not browned.

Stir in the flour and cook for about one minute to make a light roux.

Pour in the chicken broth gradually, stirring constantly until smooth.

Add the wild rice and bring the soup to a simmer.

Add the diced chicken, dried thyme, salt, and pepper.

Simmer gently until the wild rice is tender and the chicken is cooked through, about 45 minutes.

Stir in the heavy cream and heat through without boiling.

Taste and adjust seasoning as needed, then ladle into bowls and serve warm.