  We predict spontaneous generation of superfluid polariton currents in planar
microcavities with lateral periodic modulation of both potential and decay
rate. A spontaneous breaking of spatial inversion symmetry of a polariton
condensate emerges at a critical pumping, and the current direction is
stochastically chosen. We analyse the stability of the current with respect to
the fluctuations of the condensate. A peculiar spatial current domain structure
emerges, where the current direction is switched at the domain walls, and the
characteristic domain size and lifetime scale with the pumping power.
