  Despite previous intensive ground-based imaging and spectroscopic campaigns
and wide-band HST imaging of the z=0.927 QSO 3C336 field, the galaxy that hosts
the damped Ly-alpha system along this line-of-sight has eluded detection. We
present a deep narrow-band H-alpha image of the field of this z=0.656 damped
Ly-alpha absorber, obtained through the F108N filter of NICMOS 1 onboard the
Hubble Space Telescope. The goal of this project was to detect any H-alpha
emission 10 times closer than previous studies to unveil the damped absorber.
We do not detect H-alpha emission between 0.05'' and 6'' (0.24 and 30 $h^{-1}$
kpc) from the QSO, with a 3-sigma flux limit of $3.70 \times 10^{-17} h^{-2}$
erg/s/cm^2 for an unresolved source, corresponding to a star formation rate
(SFR) of $0.3 h^{-2}$ M_sun/yr. This leads to a 3-sigma upper limit of 0.15
M_sun/yr/kpc^2 on the SFR density, or a maximum SFR of 1.87 M_sun/yr assuming a
disk of 4 kpc in diameter. This result adds to the number of low redshift
damped Ly-alpha absorbers that are not associated with the central regions of
Milky-Way-like disks. Damped Ly-alpha absorption can arise from high density
concentrations in a variety of galactic environments including some that,
despite their high local HI densities, are not conducive to widespread star
formation.
