In a medium saucepan, combine wild rice and 3 cups water. Bring to a boil, then reduce heat, cover, and simmer for 45 minutes until rice is tender. Drain any excess water and set aside.
In a large pot or Dutch oven, melt butter over medium heat. Add onion, carrots, and celery; cook until softened, about 5 minutes. Add garlic and cook for 1 minute.
Sprinkle flour over vegetables and stir to coat. Cook for 2 minutes, stirring constantly.
Gradually pour in chicken broth while stirring to prevent lumps. Bring to a boil, then reduce heat and simmer for 10 minutes until slightly thickened.
Add cooked wild rice, shredded chicken, heavy cream, thyme, salt, and pepper. Stir well and heat through for about 5 minutes. Do not boil.
Taste and adjust seasoning if needed. Serve hot, garnished with fresh parsley.
Tips
For a lighter version, substitute half-and-half for heavy cream.
Store leftovers in an airtight container in the refrigerator for up to 3 days. The soup will thicken upon standing; thin with a little broth when reheating.
To freeze, omit the cream and add it after thawing and reheating.