Inelastic neutron scattering measurements demonstrate that the magnetic interactions in antiferromagnetic LaFeAsO are two dimensional. Spin-wave velocities within the Fe layer and the magnitude of the spin gap are similar to the AFe2As2 based materials. However, the ratio of interlayer and intralayer exchange is found to be less than ∼10−4 in LaFeAsO, very similar to the cuprates, and ∼100 times smaller than that found in AFe2As2 compounds. The results suggest that the effective dimensionality of the magnetic system is highly variable in the parent compounds of the iron arsenides and weak three-dimensional interactions may limit the maximum attainable superconducting Tc.