  Using galaxies as background light sources to map the Lya absorption lines is
a novel approach to study Damped Lya Absorbers (DLAs). We report the discovery
of an intervening z = 3.335 +- 0.007 DLA along a galaxy sight-line identified
among 80 Lyman Break Galaxy (LBG) spectra obtained with our Very Large
Telescope/Visible Multi-Object Spectrograph survey in the SSA22 field. The
measured DLA neutral hydrogen (HI) column density is log (NHI/cm^{-2}) = 21.68
+- 0.17. The DLA covering fraction over the extended background LBG is > 70% (2
sigma), yielding a conservative constraint on the DLA area of > 1 kpc^2. Our
search for a counterpart galaxy hosting this DLA concludes that there is no
counterpart galaxy with star formation rate (SFR) larger than a few Msun
yr^{-1}, ruling out an unobscured violent star formation in the DLA gas cloud.
We also rule out the possibility that the host galaxy of the DLA is a passive
galaxy with Mstar > 5 x 10^{10} Msun or a heavily dust-obscured galaxy with
E(B-V) > 2. The DLA may coincide with a large-scale overdensity of the
spectroscopic LBGs. The occurrence rate of the DLA is compatible with that of
DLAs found in QSO sight-lines.
