The relic abundance of light millicharged particles (MCPs) with the electric charge e′ = 5 × 10–5e and with the mass slightly below or above the electron mass is calculated. The abundance depends on the mass ratio η = mX/me and for η < 1 can be high enough to allow MCPs to be the cosmological dark matter or to make a noticeable contribution to it. On the other hand, for η ≳ 1 the cosmological energy density of MCPs can be quite low, ΩXh0 2 ≈ 0.02 for scalar MCPs, and ΩXh0 2 ≈ 0.001 for spin 1/2 fermions. But even the lowest value of ΩXh0 2 is in tension with several existing limits on the MCP abundances and parameters. However, these limits have been derived under some natural or reasonable assumptions on the properties of MCPs. If these assumptions are relaxed, a patch in the mass–charge plot of MCPs may appear, permitting them to be dark matter particles.