Monte Carlo simulations are used to show that the orientational ordering transition of planar quadrupoles on a triangular lattice is first order. The orientational ground state is a herringbone structure, and the transition lies in the universality class of a (n=3, d=2) Heisenberg model with face-oriented cubic anisotropy. The Monte Carlo results are related to recent low-energy electron-diffraction studies of N2 on graphite. Domainwall motion and the applicability of this model to herringbone phases of liquid crystals are also discussed.