The current shot-noise of an electron beam is proportional to its average current and the frequency bandwidth. This is a consequence of the Poisson distribution statistics of particles emitted at random from any source. Here we demonstrate noise suppression below the shot-noise limit in optical frequencies for relativistic electron beams. This process is made possible by collective Coulomb interaction between the electrons of a cold intense beam during beam drift. The effect was demonstrated by measuring a reduction in optical transition radiation power per unit of electron-beam pulse charge. This finding indicates that the beam charge homogenizes owing to the collective interaction, and its distribution becomes sub-Poissonian. The spontaneous radiation emission from such a beam would also be suppressed (Dicke's subradiance). Therefore, the incoherent spontaneous radiation power of any electron-beam radiation source (such as free-electron lasers) can be suppressed, and the classical coherence limits of seed-injected free-electron lasers may be surpassed.