Off the coast of India are 1,192 islands that make up the Maldives, of which 200 are inhabited, 120 are dominated by registered resorts, and one — just one— is privately owned. If the name “Coco Privé” is unfamiliar, well, that's intentional. No larger than two soccer fields, this gumdrop of paradise caters to Saudi royals and Hollywood celebrities who have managed to stay off the radar.