The existence of fractional charges carrying the current is experimentally demonstrated. Using a 2-D electron system in high perpendicular magnetic field, we measure the Shot-Noise associated with tunneling in the fractional quantum Hall regime at Landau level filling factor 1/3. The noise gives a direct determination of the quasiparticle charge, which is found to be e*=e/3, as predicted by Laughlin. The existence of e/3 Laughlin quasiparticles is unambiguously confirmed by the Shot-Noise to Johnson-Nyquist cross-over found for temperature Teta=e*V/2k.