Brown the sausage in a skillet over medium heat, breaking it up as it cooks. Drain any excess fat and set the sausage aside.
Add the onion and celery to the same skillet. Cook for 3 to 4 minutes until the vegetables soften.
In a large mixing bowl, combine the bread cubes, cooked sausage, onion and celery mixture, chestnuts, sage, thyme, parsley, salt, and pepper.
Pour the chicken broth and melted butter over the bread mixture. Stir gently until everything is evenly moistened.
Transfer the mixture to the slow cooker. Cover and cook on low for 3 to 4 hours until the stuffing is heated through and lightly set at the edges.