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Photoluminescence (PL) emission arising due to recombination of excitons in conventional semiconductors is usually unpolarized because of scattering by collective modes during exciton thermalization. Here on the contrary, we observe almost perfectly polarization-preserving PL peak centered at 2.3 eV from the surface of an archetypical three-dimensional topological insulator (TI), Bi₂Se₃. Based on the dependences of the PL spectra on the energy and polarization of incident photons, we propose that the observed PL can be semi-quantitatively explained by composite particles – chiral excitons – formed by the Coulomb attraction between massless (Dirac) electrons and massive holes, both subject to strong spin-orbit coupling which locks their spins and momenta into chiral textures. We experimentally demonstrate that the chiral excitons can be optically oriented with circularly polarized light in a broad range of excitation energies between 2.5 to 2.8 eV, and that the orientation remains preserved even at room temperature.