We present the first experimental evidence for the existence of an electron glass. The glassy relaxation is monitored by time dependent conductance measurements following an excitation of electrons to conditions far from equilibrium. At low temperatures the samples exhibit memory-effects observable for hours, as is characteristic of glasses, demonstrating the existence of a glassy electronic phase. A simple model, based on the dynamics of non-interacting Anderson-localized electrons, is analyzed to show that dynamic constraints imposed by particle conservation alone can indeed exhibit the observed non-ergodic behavior.