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 T_c.