We present accurate quantal rate constants for the D + H-2 system in the 167-900 K temperature range and rate constants calculated in the separable rotation approximation up to 1500 K. We have calculated rate constants for the three most accurate ab initio potential energy surfaces. The separable-rotation calculations agree to within 2.2% with the present accurate quantal calculations, and the results show substantially better agreement with high-temperature experimental rate constants than do previous quantal calculations. The ab initio rate constants for the LSTH and DMBE surfaces agree well with experiment over a wide temperature range; but the newer BKMP surface gives poor agreement at low temperatures. From 200 to 900 K, a factor of 4.5 in temperature, the present totally ab initio reaction rate constants agree with experiment within 13% or better at each temperature, with an average absolute deviation of only 5%.