  Damped Lyman-{\alpha} Absorbers (DLAs) as a class of QSO absorption-line
systems are currently our most important source of detailed information on the
cosmic chemical evolution of galaxies. However, the degree to which this
information is biased by dust remains to be understood. One strategy is to
specifically search for QSOs reddened by metal-rich and dusty foreground
absorbers. In this Letter we present the discovery of a z=2.60 QSO strongly
reddened by dust in an intervening extremely-strong DLA at z=2.226. This QSO
was identified through a novel selection combining the astrometric measurements
from ESA's Gaia satellite with extent optical and near/mid-infrared photometry.
We infer a total neutral atomic-hydrogen column density of log
N(HI)=21.95{\pm}0.15 and a lower limit on the gas-phase metallicity of
[Zn/H]>-0.96. This DLA is also remarkable in exhibiting shielded neutral gas
witnessed in CI and tentative detections of CO molecular bands. The Spectral
Energy Distribution (SED) of the QSO is well-accounted for by a normal QSO-SED
reddened by dust from a DLA with a 10%-of-Solar metallicity, dust extinction of
A_V=0.82{\pm}0.02mag, and LMC-like extinction curve including the
characteristic 2175{\AA} extinction feature. Such QSO absorption-line systems
have shown to be very rare in previous surveys, which have mostly revealed
sight-lines with low extinction. The present case therefore suggests that
previous samples have under-represented the fraction of dusty absorbers.
Building a complete sample of such systems is needed to assess the significance
of this effect.
