Combine the wild-rice blend with 3 cups broth and simmer covered for 35 to 40 minutes until tender.
Melt the butter in a Dutch oven and cook the onion, celery and carrot for 7 minutes until softened.
Stir in the flour for 2 minutes, then whisk in the remaining broth and milk.
Add the salt, thyme and black pepper and simmer for 8 minutes until lightly thickened.
Fold in the cooked rice and chicken and simmer gently for 8 to 10 minutes.
Heat the chicken to 165°F and thin with additional broth if the rice absorbs too much liquid.