We have determined the internal-state distribution for the HD product of the reaction of gas-phase D atoms with H atoms chemisorbed on Cu(111) and for the corresponding reaction of H atoms with chemisorbed D atoms. In the case of D-on-H, the populations of the vibrational states upsilon=0, 1, 2, and 3 are comparable, while that for upsilon=4 is considerably smaller, giving a mean vibrational energy of similar to 0.7 eV. The vibrational state distribution for H-on-D is similar, but in this case there is a clear peak at upsilon=1, even less population in upsilon=4, and a somewhat smaller mean vibrational energy of similar to 0.6 eV. The mean rotational energy falls with increasing upsilon in both cases, similar to 0.5 eV for upsilon=0 to <0.2 eV for upsilon=4, with an overall mean rotational energy of similar to 0.4 eV. The rotational distributions are distinctly narrower for H-on-D than for D-on-H. The maximum internal energy observed is similar to 2.3 eV, consistent with the total energy available to the product. Results are consistent with recent calculations.