We present a new Hubble Space Telescope (HST) Cosmic Origins Spectrograph (COS) absorption-line survey to study halo gas around 16 luminous red galaxies (LRGs) at z=0.21-0.55. The LRGs are selected uniformly with stellar mass Mstar>1e11 Msun and no prior knowledge of the presence/absence of any absorption features. Based on observations of the full Lyman series, we obtain accurate measurements of neutral hydrogen column density N(HI) and find that high-N(HI) gas is common in these massive quiescent halos with a median of <log N(HI)> = 16.6 at projected distances d<~160 kpc. We measure a mean covering fraction of optically-thick gas with log N(HI)>~17.2 of <kappa>LLS=0.44^{+0.12}_{-0.11} at d<~160 kpc and <kappa>LLS=0.71^{+0.11}_{-0.20} at d<~100 kpc. The line-of-sight velocity separations between the HI absorbing gas and LRGs are characterized by a mean and dispersion of <v_{gas-gal}>=29 km/s and sigma_v_{gas-gal}=171 km/s. Combining COS FUV and ground-based echelle spectra provides an expanded spectral coverage for multiple ionic transitions, from low-ionization MgII and SiII, to intermediate ionization SiIII and CIII, and to high-ionization OVI absorption lines. We find that intermediate ions probed by CIII and SiIII are the most prominent UV metal lines in LRG halos with a mean covering fraction of <kappa(CIII)>_{0.1}=0.75^{+0.08}_{-0.13} for W(977)>=0.1 Ang at d<160 kpc, comparable to what is seen for CIII in L* and sub-L* star-forming and red galaxies but exceeding MgII or OVI in quiescent halos. The COS-LRG survey shows that massive quiescent halos contain widespread chemically-enriched cool gas and that little distinction between LRG and star-forming halos is found in their HI and CIII content.
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