Begin by heating the olive oil in a large skillet over medium heat. Add the diced onion, sliced carrots, and celery, cooking until the onions become translucent and the vegetables soften, about 5 minutes. Stir in the minced garlic and let it cook for another minute until fragrant.
Transfer the sautéed vegetables to the slow cooker. Add the rinsed wild rice, dried thyme, dried parsley, salt, and pepper. Place the boneless, skinless chicken breasts on top, then pour in the chicken broth. Give everything a gentle stir to distribute the herbs and seasoning evenly.
Cover and cook on low for 6 to 7 hours or on high for 3 to 4 hours. The chicken will cook through and become tender, and the wild rice will plump up, absorbing the broth’s flavors. Resist the urge to open the lid during cooking to maintain consistent heat.
Once the cooking time is up, remove the chicken breasts from the slow cooker and shred them using two forks. Return the shredded chicken to the pot and stir to combine.
Stir in the heavy cream, mixing well to create a luscious, creamy broth. Taste and adjust seasoning with additional salt and pepper if needed. Let the soup warm through for another 10 minutes on low before serving.