Use a 4-quart slow cooker. Place the cut potatoes into the bottom of the slow cooker and place the chicken pieces on top. Sprinkle on the garlic. Pour chicken broth evenly over the contents of the slow cooker. Place broccoli florets on top of the chicken and add in shredded cheese.
Cover, and cook on low for 6-8 hours, or on high for 4 hours, or until chicken is no longer pink.