  We have carried out a high-resolution imaging search for the galaxy
associated with the damped Lyman-alpha (DLA) absorber at z=1.859 toward the
z_{em}=2.48 quasar QSO 1244+3443, using the HST and the NICMOS. Images were
obtained in the broad filter F160W and the narrow filter F187N with camera 2 on
NICMOS with the goal of detecting the rest-frame optical continuum and the
H-alpha line emission from the DLA. After PSF subtraction, two weak features
are seen at projected separations of 0.16-0.24" from the quasar. Parts of these
features may be associated with the DLA absorber, although we cannot completely
rule out that they could be artifacts of the point spread function (PSF). If
associated with the DLA, the objects would be ~1-2 h_{70}^{-1} kpc in size with
integrated flux densities of 2.5 and 3.3 mu Jy in the F160W filter, implying
luminosities at lambda_{central}=5600 A in the DLA rest frame of 4.4-5.9 x
10^{9} h_{70}^{-2} L_{solar} at z=1.86, for q0=0.5. However, no significant
H-alpha line emission is seen from these objects, suggesting low star formation
rates (SFRs). Our 3 sigma upper limit on the SFR in the DLA is 1.3 h_{70}^{-2}
M_{solar}/yr for q0 = 0.5 (2.4 h_{70}^{-2} M_{solar} yr^{-1} for q0 = 0.1).
This together with our earlier result for LBQS 1210+1731 mark a significant
improvement over previous constraints on the star formation rates of DLAs. A
combination of low SFR and some dust extinction is likely to be responsible for
the lack of H-alpha emission. Alternatively, the objects, may be associated
with the quasar host galaxy. In any case, our observations suggest that the DLA
is not a large bright proto-disk, but a compact object or a low-surface
brightness galaxy. If the two features are PSF artifacts then the constraints
on DLA properties are even more severe.
