The Cosmic Ultraviolet Baryon Survey (CUBS) II: Discovery of an H$_{2}$-Bearing DLA in the Vicinity of an Early-Type Galaxy at z = 0.576.

We report the serendipitous detection of an H$_{2}$-bearing damped Lyman-$\alpha$ absorber at z = 0.576 in the spectrum of the QSO J0111-0316 in the Cosmic Ultraviolet Baryon Survey. Spectroscopic observations from HST-COS in the far-ultraviolet reveal a damped absorber with log[N(HI)/cm^-2] = 20.10 (-0.21, +0.25) and log[N(H$_{2}$)/cm^-2] = 18.96 +/- 0.05. The diffuse molecular gas is found in two velocity components separated by dv = 60 km/s, with >99.9% of the total H$_{2}$ column density concentrated in one component. At a metallicity of $\approx$ 40% of solar, there is evidence for Fe enhancement and dust depletion, with a dust-to-gas ratio $\kappa_{\text{O}} \approx$ 0.4. A galaxy redshift survey conducted with IMACS and LDSS-3C on Magellan reveals an overdensity of nine galaxies at projected distance d <= 600 proper kpc (pkpc) and line-of-sight velocity offset dv$_{g}$ <= 300 km/s from the absorber. The closest is a massive, early-type galaxy at d = 41 pkpc which contains 70% of the total stellar mass identified at d <= 310 pkpc of the H$_{2}$ absorber. The close proximity of the H$_{2}$-bearing gas to the quiescent galaxy and the Fe-enhanced chemical abundance pattern of the absorber suggest a physical connection, in contrast to a picture in which DLAs are primarily associated with gas-rich dwarfs. This case study illustrates that deep galaxy redshift surveys are needed to gain insight into the diverse environments that host dense and potentially star-forming gas.