We report two detections of deuterated molecular hydrogen ( HD ) in QSO absorption-line systems at z > 2 . Toward J2123-0500 , we find N ( HD ) = 13.84 \pm 0.2 for a sub-DLA with metallicity \simeq 0.5 Z _ { \odot } and N ( H _ { 2 } ) = 17.64 \pm 0.15 at z = 2.0594 . Toward FJ0812+32 , we find N ( HD ) = 15.38 \pm 0.3 for a solar-metallicity DLA with N ( H _ { 2 } ) = 19.88 \pm 0.2 at z = 2.6265 . These systems have ratios of HD to H _ { 2 } above that observed in dense clouds within the Milky Way disk and apparently consistent with a simple conversion from the cosmological ratio of D/H . These ratios are not readily explained by any available model of HD chemistry and there are no obvious trends with metallicity or molecular content . Taken together , these two systems and the two published z > 2 HD-bearing DLAs indicate that HD is either less effectively dissociated or more efficiently produced in high-redshift interstellar gas , even at low molecular fraction and/or solar metallicity . It is puzzling that such diverse systems should show such consistent HD/H _ { 2 } ratios . Without clear knowledge of all the aspects of HD chemistry that may help determine the ratio HD/H _ { 2 } , we conclude that these systems are potentially more revealing of gas chemistry than of D/H itself and that it is premature to use such systems to constrain D/H at high-redshift .