Finely dice the carrots, onion, and celery. Mince the garlic.
In a large heavy-bottomed pot, heat the olive oil over medium heat. Add the carrot, onion, and celery to pot, and saute until the onions are soft and translucent, about 8-10 minutes.
Add the garlic, black pepper, oregano, chicken stock, water, and 1 cup of milk to the pot. Stirring occasionally, allow soup to simmer on medium heat for 15 minutes.
In a small bowl, whisk together the remaining 1 cup of milk with the ½ cup flour until no lumps remain. Add mixture to the pot, and immediately stir to prevent any lumps from forming.
Add the cooked chicken, long grain and wild rice mixture, and the seasoning packet to the pot. While stirring occasionally, continue simmering soup over medium heat for 20 minutes or until the rice is tender.
Add salt and pepper to taste. Serve, and enjoy!