We present the elemental abundance and H2 content measurements of a Damped
Lyman-{\alpha} (DLA) system with an extremely large H i column density, log N(H
i) (cm-2) = 22.0+/-0.10, at zabs = 3.287 towards the QSO SDSS J 081634+144612.
We measure column densities of H2, C i, C i^*, Zn ii, Fe ii, Cr ii, Ni ii and
Si ii from a high signal-to-noise and high spectral resolution VLT-UVES
spectrum. The overall metallicity of the system is [Zn/H] = -1.10 +/- 0.10
relative to solar. Two molecular hydrogen absorption components are seen at z =
3.28667 and 3.28742 (a velocity separation of \approx 52 km s-1) in rotational
levels up to J = 3. We derive a total H2 column density of log N(H2) (cm-2) =
18.66 and a mean molecular fraction of f = 2N(H2)/[2N(H2) + N(H i)] =
10-3.04+/-0.37, typical of known H2-bearing DLA systems. From the observed
abundance ratios we conclude that dust is present in the Interstellar Medium
(ISM) of this galaxy, with a enhanced abundance in the H2-bearing clouds.
However, the total amount of dust along the line of sight is not large and does
not produce any significant reddening of the background QSO. The physical
conditions in the H2-bearing clouds are constrained directly from the column
densities of H2 in different rotational levels, C i and C i^* . The kinetic
temperature is found to be T = 75 K and the particle density lies in the range
nH = 50-80 cm-3 . The neutral hydrogen column density of this DLA is similar to
the mean H i column density of DLAs observed at the redshift of {\gamma}-ray
bursts (GRBs). We explore the relationship between GRB-DLAs and high column
density end of QSO-DLAs finding that the properties (metallicity and depletion)
of DLAs with log N(H i) > 21.5 in the two populations do not appear to be
significantly different