  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 $\simeq 0.5Z_{\odot}$ 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.
