  We study a new class of chaotic systems with dynamical localization, where
gain or loss mechanisms break the Hermiticity, while allowing for parity-time
(PT) symmetry. For a value \gamma_PT of the gain or loss parameter the spectrum
undergoes a spontaneous phase transition from real (exact phase) to complex
values (broken phase). We develop a one parameter scaling theory for \gamma_PT,
and show that chaos assists the exact PT phase. Our results have applications
to the design of optical elements with PT symmetry.
