We present accurate quantum mechanical differential cross sections for the H + D2 reaction. Results are given for two potential energy surfaces and three initial states at relative translational energies of Erel = 0.525-0.562 eV. Comparisons are made to quasiclassical trajectory simulations and experiments. The average final rotational quantum number is 12% less than the quasiclassical one, and the quantal and classical differential cross sections have qualitatively different shapes. The theoretical differential cross sections show less forward scattering than experiment.