We report on memory effects observed in the time dependence of the magnetization M(T, H) of a superconducting Y-Ba-Cu-O single crystal. As in spin-glasses, the decay rate S=dM/dlnt is not uniquely determined. It exhibits a characteristic change at time t equal to the waiting time tw during which the specimen was kept at a given temperature T<Tc and magnetic field H before a field perturbation ΔH is applied at time t=0. This phenomenon, seen for the first time in a superconductor, reveals the glassy nature of the superconducting state in the high-Tc oxides.