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 graphite. 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 a "domain size" are all shown to obey the Allen-Cahn law. This is in disagreement with the interpretation of an earlier Monte Carlo study of the same model.