  We show that the relic abundance of thermal dark matter annihilating via a
long-range interaction, is significantly affected by the formation and decay of
dark matter bound states in the early universe, if the dark matter mass is
above a few TeV. We determine the coupling required to obtain the observed dark
matter density, taking into account both the direct 2-to-2 annihilations and
the formation of bound states, and provide an analytical fit. We argue that the
unitarity limit on the inelastic cross-section is realized only if dark matter
annihilates via a long-range interaction, and we determine the upper bound on
the mass of thermal-relic dark matter to be about 197 (139) TeV for
(non)-self-conjugate dark matter.
