Neutron diffraction techniques have been used to investigate the magnetic ordering of the Tb ions in polycrystalline Pb2Sr2TbCu3O8. Significant magnetic correlations are found to develop below approximately 10 K, and these correlations are two dimensional in nature, representative of the strongly anisotropic magnetic interactions in these layered materials. The correlation length increases with decreasing temperature, and long-range order is observed to develop at T(N) almost-equal-to 5.5 K. However, the sawtooth Bragg profile for the scattering demonstrates that the long-range order is two dimensional, rather than three dimensional, with a spin configuration where nearest-neighbor spins are antiparallel The scattering profile can be explained quantitatively by assuming long-range order within the ab plane, with no significant correlations along the c axis to the lowest temperatures measured (1.36 K). Our results suggest that the system is well described by a two-dimensional Ising model. The only other (pure) system where a crossover to three-dimensional behavior is not observed is DyBa2Cu4O8.