Conditions for existence of the L3 phase have been determined for a system containing water, n-hexanol, and the zwitterionic surfactant n-tetradecyldimethylamineoxide. Electric birefringence, light-scattering, rheology, and electrical-conductivity experiments were performed on this phase. Results are consistent with the existence of platelike micelles, whose diameter changes with surfactant concentration in such a way that it remains comparable to mean plate spacing. This behavior can be understood in terms of a previous L3 phase theory containing randomly oriented plates.