Grease a 4- to 6-quart slow cooker with the coconut oil.
Add the chicken thigh pieces to the slow cooker. Add the garlic, chilies, ginger, erythritol sweetener, if using, fish sauce, lemongrass, and chicken broth.
Cover and cook on LOW for 4 hours.
Five minutes before serving, stir in the coconut milk and lime juice. Top with the parsley and serve.