Put chicken in a large saucepan and add 1.5 quarts water; it should be enough to cover the chicken by at least 1 inch. Add remaining ingredients in step 1. Bring to a boil, then turn down to a simmer and cook for 15-30 minutes. Chicken is done when it is tender, 165 degrees and not pink in the center.
Remove chicken from pot, discard vegetables and reserve broth in case it's needed in the future to thin the cream of chicken and wild rice soup. Shred the chicken into bite sized chunks. Cover and set aside until needed.
Step 2: Prepare Cream of Chicken and Wild Rice Soup
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.
Notes
If you like more rice in your soup, you can add 2 boxes of Rice-a-Roni. Test the flavor of the broth after you add one seasoning packet to determine whether you want the additional seasoning of the second packet.
Be sure to stir the cream of chicken and rice soup frequently, as it can get stuck to the bottom of your pan.
Store in pot with lid on it or in airtight container in the refrigerator for up to 3 days. Soup will thicken in the refrigerator; you can thin it out with your reserved broth, water or milk.
You can freeze it in an airtight freezer container for up to 2 months, but the creamy soup might break down upon reheating from the freezer. Reheat very slowly over a low heat, and whisk to return it to proper consistency.