We report the observation of spin currents in a coherent gas of indirect excitons. The realized long-range spin currents originate from the formation of a coherent gas of bosonic pairs--a new mechanism to suppress the spin relaxation. The spin currents result in the appearance of a variety of polarization patterns, including helical patterns, four-leaf patterns, spiral patterns, bell patterns, and periodic patterns. We demonstrate control of the spin currents by a magnetic field. We also present a theory of coherent exciton spin transport that describes the observed exciton polarization patterns and indicates the trajectories of the spin currents.