In a large pot over medium heat, sauté onions, carrots, and celery for about 5 minutes until softened.
Add garlic, thyme, and black pepper; cook for an additional minute until fragrant.
Incorporate the diced chicken and cook until no longer pink, about 5-7 minutes.
Stir in the wild rice and chicken broth; bring to a boil, then reduce heat to simmer.
Cover and simmer for about 45 minutes, or until rice is tender.
Once the rice is tender, stir in the heavy cream and season with salt to taste.
Serve hot, garnished with fresh herbs if desired.