In a large pot or Dutch oven, heat olive oil over medium heat.
Add the onion, celery, and carrots. Sauté for 5–7 minutes until softened.
Stir in garlic and cook for 1 minute until fragrant.
Pour in chicken broth, then add shredded chicken, cooked wild rice, thyme, salt, and pepper.
Bring the soup to a gentle boil, then reduce heat and simmer for 15–20 minutes.
Stir in the half-and-half or cream and heat through for another 5 minutes.
Taste and adjust seasonings if needed. Serve hot with bread or crackers.