We have measured the nascent HD(v′=1, j′) product rotational distribution from the reaction D+H2(v, j) in which the H2 reagent was either thermal (v=0, j) or prepared in the level (v=1, j=1) by stimulated Raman pumping. Translationally hot D atoms were obtained by uv laser photolysis of DBr or DI. Photolysis of DBr generated D atoms with center-of-mass collision energies (Erel) of 1.04 and 0.82 eV, which corresponded to the production of ground state Br and spin–orbit-excited Br*, respectively. The Erel values for DI photolysis were 1.38 and 0.92 eV. Quantum-state-specific detection of HD was accomplished via (2+1) resonance-enhanced multiphoton ionization and time-of-flight mass spectrometry. Vibrational excitation of the H2 reagent results in substantial rotational excitation of the HD(v′=1) product and increases the reaction rate into v′=1 by about a factor of 4. Although the quantum-mechanical calculation of Blais et al. [Chem. Phys. Lett. 166, 11 (1990)] for the D+H2(v=1, j=1)→HD(v′=1, j′)+H product rotational distribution at Erel=1.02 eV is in qualitative agreement with experiment, it does not quantitatively agree with the measured distribution. Specifically, the calculated distribution is too hot by 2–3 rotational quanta, and the predicted enhancement in the v′=1 rate with reagent vibrational excitation is too large by 67%±9.