Patients receive cisplatin intravenously (IV) over 1 hour on days 1, 8, 15, 22, 29, and 36, undergo external beam radiation therapy 5 days a week for 6 weeks, and then undergo intracavitary brachytherapy for approximately 2 weeks. Within 2 weeks, patients receive ipilimumab IV over 90 minutes once every 3 weeks for 12 weeks.