Place the chicken breasts in the slow cooker. Add the chicken broth, buffalo hot sauce, diced onion, sliced carrots, sliced celery, garlic powder, salt, and black pepper.
Cover and cook on low for 6 hours until the chicken is tender and reaches an internal temperature of 165 degrees.
Remove the chicken from the slow cooker and shred it with two forks. Return the shredded chicken to the slow cooker.
Add the cubed cream cheese to the slow cooker. Stir until the cream cheese melts and blends into the broth.
Ladle the soup into bowls and top each serving with blue cheese crumbles and sliced green onions.