The development of orientational order in an anisotropic planar rotor model has been studied by Monte Carlo methods. The order develops following an instantaneous quench from a high temperature, disordered phase to an unstable low temperature state in which a threefold degenerate herringbone phase is the equilibrium state. The model describes the orientational properties of N2 molecules physisorbed on the hexagonal graphite surface and with some modifications the ordering of certain smectic phases in liquid crystals. Both the dynamical structure factor and average domain size have been determined. The structure factor is shown to satisfy dynamical scaling. The growth laws for three different measures of “domain size” are all shown to be consistent with the Allen-Cahn theory. This interpretation of the data is in disagreement with an earlier analysis of domain growth for this model.