Start by preparing the vegetables. Dice the onion, carrots, and celery into small pieces, and mince the garlic.
Place the boneless chicken breasts at the bottom of the slow cooker.
Add the diced onion, carrots, celery, and minced garlic on top of the chicken.
Rinse the wild rice under cold water, then add it to the slow cooker.
Pour in the low-sodium chicken broth, and add the dried thyme, dried rosemary, salt, and pepper. Stir gently to combine.
Cover the slow cooker with the lid. Set it to cook on low for 6 hours or on high for 3 hours, until the chicken is cooked through and the wild rice is tender.
Once cooking is complete, remove the chicken breasts, shred them with two forks, and return the shredded chicken to the soup.
If desired, stir in whole milk or heavy cream to create a creamier texture. Adjust seasonings if needed.
Serve hot, garnished with fresh parsley.