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Most known bound excitons are composed of massive electron-hole pairs, while optical excitations arising from massless quasiparticle bands, such as the Dirac cone in graphene, tend to be short-lived resonant exciton states. However, researchers have recently measured novel long-lived chiral excitons in the 3D topological insulator Bi₂Se₃, which are composed of massive holes and massless electrons, both residing on the surface state and subject to strong spin-orbit interactions. These chiral excitons exhibit both circular dichroism and almost perfectly preserved circular polarization in the photoluminescence emission caused by chiral exciton recombination. Here, we utilize the ab initio GW and GW plus Bethe Salpeter equation (GW+BSE) method to study the quasiparticle bandstructure and optical absorption spectrum including excitonic effects in both the bulk and surface of Bi₂Se₃. Our calculations are based on the fully-relativistic spinor GW-BSE formalism and reveal the nature of both excitons near the Fermi level and those arising from transitions between higher-energy surface states.