Begin by heating the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion, diced carrots, and diced celery. Sauté for about 5 minutes until the vegetables begin to soften and the onion is translucent.
Stir in the minced garlic and sauté for an additional minute, allowing the garlic to become fragrant but not browned.
Add the cubed chicken breast to the pot. Season with salt, pepper, thyme, and parsley. Cook for about 5-7 minutes, stirring occasionally, until the chicken is no longer pink.
Stir in the rinsed wild rice and the chicken broth. Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let it simmer for about 45 minutes, or until the rice is tender.
Once the rice is cooked, stir in the heavy cream. Allow the soup to heat through for about 5 minutes, stirring occasionally. Taste and adjust the seasoning with additional salt and pepper as needed.
Ladle the Creamy Chicken and Wild Rice Soup into bowls and enjoy it warm. You can garnish with additional parsley if desired for a pop of color and freshness.