We study the propagation of fast electrons in a gas at different densities. A large relativistic electron current is produced by focusing a short-pulse ultrahigh-intensity laser on a metallic target. It then propagates in a gas jet placed behind the foil. Shadowgraphy in the gas shows an electron cloud moving at sub-relativistic average velocities. The experiment shows (i) the essential role of the density of background material for allowing propagation of fast electrons, (ii) the importance of the ionization phase which produces free electrons available for the return current, and (iii) the effect of electrostatic fields on fast-electron propagation.