The growth of two-dimensional herringbone phases following quenches from high to low temperatures is analyzed by computer simulation. The herringbone ordering is threefold degenerate and governed by an anisotropic-planar-rotor model on a triangular lattice. The model describes the orientational properties of N2 on graphite. The growth with time of the average domain radius is shown to be algebraic with a rather low growth exponent n 0.25.