A c-axis magnetotransport and resistance noise study in La_{1.97}Sr_{0.03}CuO_{4} reveals clear signatures of glassiness, such as hysteresis, memory, and slow, correlated dynamics, but only at temperatures (T) well below the spin glass transition temperature T_{sg}. The results strongly suggest the emergence of charge glassiness, or dynamic charge ordering, as a result of Coulomb interactions.