Place the chicken breasts, wild rice, chicken broth, cream of chicken soup, carrots, onion, celery, thyme, garlic powder, salt, and pepper into the slow cooker.
Stir the ingredients until the soup and broth are evenly mixed with the rice and vegetables.
Cover and cook on low for 6 to 7 hours, until the rice is tender and the chicken reaches an internal temperature of 165°F.
Remove the chicken breasts from the slow cooker and shred them with two forks.
Return the shredded chicken to the slow cooker and add the cubed cream cheese.
Stir until the cream cheese melts fully and creates a creamy sauce.
Spoon the casserole into bowls and top each serving with chopped fresh parsley.