Gather all of your ingredients.

Heat the olive oil in a large pot over medium heat.

Dice the onion and mince the garlic. Add them to the hot oil and sauté until tender (about 5 minutes).

Clean and slice the carrots and celery if using fresh. Add them to the pot and cook for about 5 minutes more.

Add the whole chicken breast, bay leaf, oregano, thyme, cracked pepper, wild rice, and 6 cups of water to the pot. Do not add salt yet.

Bring the pot up to a boil over medium-high heat, then reduce the heat to low and let simmer for one hour.

Near the end of the hour, melt 2 Tbsp of butter in a small pot over medium heat.

Whisk in 2 Tbsp of all-purpose flour and cook for 2 minutes.

Whisk in the milk and allow to come up to a simmer, whisking occasionally.

Once it reaches a simmer and thickens slightly, remove from heat.

Carefully shred the chicken in the pot with two forks.

Add the thickened milk mixture and the chopped parsley to the soup.

Season with salt to taste, starting with a small amount and adding more if needed.

Serve hot.