We present a detailed analysis of a red quasar at z=2.32 with an intervening damped Lyman-alpha absorber (DLA) at z=2.13. Using high quality data from the X-shooter spectrograph at ESO Very Large Telescope we find that the absorber has a metallicity consistent with Solar. We observe strong C I and H$_2$ absorption indicating a cold, dense absorbing medium. Partial coverage effects are observed in the C I lines, from which we infer a covering fraction of $27 pm 6$ % and a physical diameter of the cloud of 0.1 pc. From the covering fraction and size, we estimate the size of the background quasars broad line region. We search for emission from the DLA counterpart in optical and near-infrared imaging. No emission is observed in the optical data. However, we see tentative evidence for a counterpart in the H and K band images. The DLA shows high depletion (as probed by [Fe/Zn]=-1.22) indicating that significant amounts of dust must be present in the DLA. By fitting the spectrum with various dust reddened quasar templates we find a best-fitting amount of dust in the DLA of $A(V)_{rm DLA}=0.28 pm 0.01|_{rm stat} pm 0.07|_{rm sys}$. We conclude that dust in the DLA is causing the colours of this intrinsically very luminous background quasar to appear much redder than average quasars, thereby not fulfilling the criteria for quasar identification in the Sloan Digital Sky Survey. Such chemically enriched and dusty absorbers are thus underrepresented in current samples of DLAs.
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