An analysis of a two-dimensional tidal model of the Wadden Sea reveals Lagrangian chaos in the trajectories of water parcels. The associated chaotic stirring results from the transverse intersection of the stable and unstable curves of hyperbolic fixed points in the Lagrangian residual displacement field (the tidal Poincaré map). This tidal dispersion mechanism produces rapid water exchange along the channel axis and could be representative of many shallow tidal seas.