Using simulations of hard rods in smectic-A states, we find stringlike clusters of up to 10 interlayer rods exhibiting dynamic cooperativity. We also find non-gaussian diffusion and heterogeneous dynamics due to the equilibrium periodic smectic density profiles, which give rise to permanent barriers for layer-to-layer diffusion. This relaxation behavior is surprisingly similar to that of nonequilibrium supercooled liquids, although there the particles are trapped in transient (instead of permanent) cages.