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We report a NOrthern Extended Millimeter Array (NOEMA) and Atacama LargeMillimeter/submillimeter Array (ALMA) search for redshifted CO emission fromthe galaxies associated with seven high-metallicity ([M/H] $\geq -1.03$) dampedLyman-$\alpha$ absorbers (DLAs) at $z\approx1.64-2.51$. Our observationsyielded one new detection of CO(3-2) emission from a galaxy at $z=2.4604$ usingNOEMA, associated with the $z=2.4628$ DLA towards QSO B0201+365. Includingprevious searches, our search results in detection rates of CO emission of$\approx56^{+38}_{-24}$ % and $\approx11^{+26}_{-9}$ %, respectively, in thefields of DLAs with ${\rm [M/H]}>-0.3$ and ${\rm [M/H]}<-0.3$. Further, theHI-selected galaxies associated with five DLAs with [M/H] $>-0.3$ all have highmolecular gas masses, $\gtrsim5\times10^{10}\ {\rm M}_\odot$. This indicatesthat the highest-metallicity DLAs at $z\approx2$ are associated with the mostmassive galaxies. The newly-identified $z\approx2.4604$ HI-selected galaxy,DLA0201+365g, has an impact parameter of $\approx7$ kpc to the QSO sightline,and an implied molecular gas mass of $(5.04\pm0.78)\times10^{10}\times(\alpha_{\rm CO}/4.36)\times(r_{31}/0.55)\ {\rm M}_\odot$.Archival Hubble Space Telescope Wide Field and Planetary Camera 2 imagingcovering the rest-frame near-ultraviolet (NUV) and far-ultraviolet (FUV)emission from this galaxy yield non-detections of rest-frame NUV and FUVemission, and a $5\sigma$ upper limit of 2.3 M$_\odot$ yr$^{-1}$ on theunobscured star formation rate (SFR). The low NUV-based SFR estimate, despitethe very high molecular gas mass, indicates that DLA0201+365g either is a verydusty galaxy, or has a molecular gas depletion time that is around two ordersof magnitude larger than that of star-forming galaxies at similar redshifts.

A Massive, Dusty HI-Absorption-Selected Galaxy at $z \approx 2.46$ Identified in a CO Emission Survey