A neutral collisionless particle X with a mass of the order of 1 GeV has previously been proposed as a possible dark matter candidate . The present work investigates whether such a particle could have been produced during the primordial electron–positron epoch of the early Universe. A production mechanism based on electron–positron annihilation and involving both virtual-photon and dark-photon intermediate states is considered. It is shown that quantum interference between the two channels may generate a small primordial X–Xˉ asymmetry, preventing complete annihilation of the produced pairs. The surviving relic population is found to be of the same order of magnitude as the dark matter density inferred from cosmological observations.