While chicken is cooking, put olive oil in a 4 quart stock pot and add diced carrots, celery and onion. Bring to a low simmer over medium heat and cook for 8-10 minutes, until vegetables begin to soften and onion is translucent.
Stir in garlic, chicken broth, water, and 1 cup of milk.
Mix in bay leaf, oregano and black pepper. Bring mixture to a simmer and continue simmering for 15 minutes.
Whisk flour into remaining cup of milk until completely smooth. Once you're sure there are no lumps in the mixture, pour it into the soup and stir to thoroughly incorporate.
Add the box of long grain & wild rice to the soup, including the seasoning packet. Stir until combined.
Add in the shredded chicken. Simmer for 25-30 minutes until rice is tender.
Remove bay leaf and season with salt and pepper to taste.