Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery and cook for 5 minutes until the vegetables begin to soften.
Stir in the garlic and cook for 1 minute. Add the chicken pieces and cook until they are no longer pink on the outside, about 4 minutes.
Pour in the chicken broth. Add the wild rice, thyme, bay leaves, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 45 minutes. Stir once or twice during cooking to prevent the rice from sticking.
Remove the bay leaves. Taste and adjust salt if needed. Sprinkle with fresh parsley before serving.