We analyze new far-ultraviolet spectra of 13 quasars from the z~0.2 COS-Halos survey that cover the HI Lyman limit of 14 circumgalactic medium (CGM) systems. These data yield precise estimates or more constraining limits than previous COS-Halos measurements on the HI column densities NHI. We then apply a Monte-Carlo Markov Chain approach on 32 systems from COS-Halos to estimate the metallicity of the cool (T~10^4K) CGM gas that gives rise to low-ionization state metal lines, under the assumption of photoionization equilibrium with the extragalactic UV background. The principle results are: (1) the CGM of field L* galaxies exhibits a declining HI surface density with impact parameter Rperp (at >99.5%$ confidence), (2) the transmission of ionizing radiation through CGM gas alone is 70+/-7%; (3) the metallicity distribution function of the cool CGM is unimodal with a median of 1/3 Z_Sun and a 95% interval from ~1/50 Z_Sun to over 3x solar. The incidence of metal poor (<1/100 Z_Sun) gas is low, implying any such gas discovered along quasar sightlines is typically unrelated to L* galaxies; (4) we find an unexpected increase in gas metallicity with declining NHI (at >99.9% confidence) and, therefore, also with increasing Rperp. The high metallicity at large radii implies early enrichment; (5) A non-parametric estimate of the cool CGM gas mass is M_CGM_cool = 9.2 +/- 4.3 10^10 Msun, which together with new mass estimates for the hot CGM may resolve the galactic missing baryons problem. Future analyses of halo gas should focus on the underlying astrophysics governing the CGM, rather than processes that simply expel the medium from the halo.
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