In a large pot or Dutch oven, heat the olive oil over medium heat. Add the onions, carrots, celery, and garlic. Sauté until the vegetables are slightly softened, about 5 minutes.

Add the cubed chicken to the pot and cook until it's no longer pink, about 6-8 minutes.

Rinse the wild rice under cold water and drain. Add the wild rice, chicken broth, dried thyme, bay leaf, salt, and pepper to the pot. Bring the mixture to a boil.

Reduce the heat to low, cover the pot, and let the soup simmer for about 45-50 minutes, or until the rice is tender and cooked through.

Once the soup is ready, remove the bay leaf and taste for seasoning. Adjust the salt and pepper if needed.

Ladle the soup into bowls, garnish with fresh parsley if desired, and serve hot.