We observe composite particles -- chiral excitons -- residing on the surface of a topological insulator (TI), Bi2Se3. Unlike other known excitons composed of massive quasiparticles, chiral excitons are the bound states of surface massless electrons and surface massive holes, both subject to strong spin–orbit coupling which locks their spins and momenta into chiral textures. Due to this unusual feature, chiral excitons emit circularly polarized secondary light (photoluminescence) that conserves the polarization of incident light. This means that the out-of-plane angular momentum of a chiral exciton is preserved against scattering events during thermalization, thus enabling optical orientation of carriers even at room temperature. The discovery of chiral excitons adds to the potential of TIs as a platform for photonics and optoelectronics devices.