  We image 19 quasars with 22 damped Lyman alpha (DLA) systems using the F160W
filter and the Near-Infrared Camera and Multiobject Spectrograph aboard the
Hubble Space Telescope, in both direct and coronagraphic modes. We reach 5
sigma detection limits of ~H=22 in the majority of our images. We compare our
observations to the observed Lyman-break population of high-redshift galaxies,
as well as Bruzual & Charlot evolutionary models of present-day galaxies
redshifted to the distances of the absorption systems. We predict H magnitudes
for our DLAs, assuming they are producing stars like an L* Lyman-break galaxy
(LBG) at their redshift. Comparing these predictions to our sensitivity, we
find that we should be able to detect a galaxy around 0.5-1.0 L* (LBG) for most
of our observations. We find only one new possible candidate, that near
LBQS0010-0012. This scarcity of candidates leads us to the conclusion that most
DLA systems are not drawn from a normal LBG luminosity function nor a local
galaxy luminosity function placed at these high redshifts.
