We study kagome lattice antiferromagnets where the effects of easy-axis single-ion anisotropy (D) dominates over the Heisenberg exchange J. For S> or =3/2, virtual quantum fluctuations help lift the extensive classical degeneracy. We demonstrate the presence of a one-third magnetization plateau for a broad range of magnetic fields J3/D2 < or = B < or = JS along the easy axis. The fully equilibrated system at low temperature on this plateau develops an unusual nematic order that breaks sublattice rotation symmetry but not translation symmetry; however, extremely slow dynamics associated with this ordering is expected to lead to glassy freezing of the system on intermediate time scales.