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We report the discovery of large amounts of cold (T ~ 104 K), chemically young gas in an overdensity of galaxies at redshift z ≈ 1.6 located in the Great Observatories Origins Deep Survey southern field. The gas is identified thanks to the ultra-strong Mg II λ2800 absorption features it imprints onto the rest-frame UV spectra of galaxies in the background of the overdensity. There is no evidence that the optically thick gas is part of any massive galaxy (i.e., Mstar > 4 x 109 M⊙), but rather is associated with the overdensity; less massive and fainter galaxies (25.5 mag < z < 27.5 mag) have too large an impact parameter to be causing ultra-strong absorption systems, based on our knowledge of such systems. The lack of corresponding Fe II absorption features, not detected even in co-added spectra, suggests that the gas is chemically more pristine than the interstellar medium and outflows of star-forming galaxies at similar redshift, including the galaxies of the overdensity itself, and comparable to the most metal-poor stars in the Milky Way halo. A crude estimate of the projected covering factor of the high-column-density gas (NH ≳ 1020 cm-2) based on the observed fraction of galaxies with ultra-strong absorbers is CF ≈ 0.04. A broad, continuum absorption profile extending to the red of the interstellar Mg II absorption line by ≲2000 km s-1 is possibly detected in two independent co-added spectra of galaxies belonging to the overdensity, consistent with a large-scale infall motion of the gas onto the overdensity and its galaxies. Overall, these findings provide the first tentative evidence of accretion of cold, chemically young gas onto galaxies at high redshift, possibly feeding their star formation activity. We suggest the tact that the galaxies are members of a large structure, as opposed to field galaxies, might play a significant role in our ability to detect the accreting gas. [ABSTRACT FROM AUTHOR]