Drizzle olive oil in a deep dish pot or dutch oven. Place the pot on medium high heat. Add the celery, carrots, onions and garlic. Sauté the ingredients until everything starts to soften and brown a little bit. This should take about 10 minutes.
Add the chicken breast to the pan on top of the cooked veggies. Season the chicken with salt, pepper oregano and two bay leaves. Pour the broth 1 cup milk and 1/2 cup heavy cream into the pot, followed by the wild rice. Lastly, add the contents of the seasoning packet.
Give everything a quick mix. Bring the pot up to a boil over high heat, then lower it to a simmer. Cover and cook for about 20 minutes.
While the rice and chicken are cooking, make a thickening mixture. Combine flour, remaining milk and heavy cream using a whisk. Set aside.
Remove the bay leaves from the soup and discard. Next, remove the chicken from the soup and shred with a fork. Add the shredded chicken back into the soup, followed by the thickener, let simmer for 5 minutes until it thickens. Mix everything together. Serve hot and enjoy!