High energy particles traversing the Universe through the cosmic microwave backgroung radiation can, in principle, emit Cherenkov radiation. It is shown that the energy threshold for this radiation is extremely high and its intensity would be too low due to the low density of the "relic photons gas" and very weak interaction of two photons.

6 pages, LATEX, no Figs.; to be published in JETP Lett. 75 (N4) (2002)