  We report the detection of H_2, CI, CI*, CI** and Cl I lines in a near
Solar-metallicity ([Zn/H]=-0.13) damped Lyman-alpha (DLA) system at z_abs=1.962
observed on the line of sight to the quasar Q 0551-366. The iron-peak elements,
X=Fe, Cr and Mn are depleted compared to zinc, [X/Zn] -0.8, probably because
they are tied up onto dust grains. Among the three detected H_2-bearing clouds,
spanning 55 km s^-1 in velocity space, we derive a total molecular hydrogen
column density N(H_2)=2.6x10^17 cm^-2 and a mean molecular fraction
f=2N(H_2)/(2N(H_2)+N(HI))=1.7x10^-3. The depletion of heavy elements (S, Si,
Mg, Mn, Cr, Fe, Ni and Ti) in the central component is similar to that observed
in the diffuse neutral gas of the Galactic halo. This depletion is
approximately the same in the six CI-detected components independently of the
presence or absence of H_2. The gas clouds in which H_2 is detected always have
large densities, n_H>30 cm^-3, and low temperatures, T_01<~100 K. This shows
that presence of dust, high particle density and/or low temperature are
required for molecules to be present. The photo-dissociation rate derived in
the components where H_2 is detected suggests the existence of a local UV
radiation field similar in strength to the one in the Galaxy. Star formation
therefore probably occurs near these H_2-bearing clouds.
