Lightly spray the insert of a six-quart slow cooker with nonstick cooking spray.
Place the boneless skinless chicken breasts in a single layer across the bottom of the slow cooker.
In a medium mixing bowl, stir together the cream of chicken soup, sour cream, and chicken broth until smooth.
Spread the cream of chicken mixture evenly over the chicken breasts.
Sprinkle the dry stuffing mix evenly over the creamy sauce. Gently press the stuffing into the sauce with the back of a spoon. Do not completely stir everything together.
Cover and cook on LOW for four to five hours, or until the chicken reaches an internal temperature of 165°F and is tender.
Leave the chicken breasts whole for serving, or shred the cooked chicken with two forks and gently stir it into the stuffing and sauce.
Allow the chicken and stuffing to rest for five minutes before serving.