We present the results from our COS circumgalactic medium (CGM) compendium (CCC), a survey of the CGM at z<~1 using HI-selected absorbers with 15<logN_HI_<19. We focus here on 82 partial Lyman limit systems (pLLSs, 16.2<=logN_HI_<17.2) and 29 LLSs (17.2<=logN_HI_<19). Using Bayesian techniques and Markov Chain Monte Carlo sampling of a grid of photoionization models, we derive the posterior probability distribution functions (PDFs) for the metallicity of each absorber in CCC. We show that the combined pLLS metallicity PDF at z<~1 has two main peaks at [X/H]~-1.7 and -0.4, with a strong dip at [X/H]~-1. The metallicity PDF of the LLSs might be more complicated than a unimodal or bimodal distribution. The pLLSs and LLSs probe a similar range of metallicities -3<~[X/H]<~+0.4, but the fraction of very metal-poor absorbers with [X/H]<~-1.4 is much larger for the pLLSs than the LLSs. In contrast, absorbers with logN_HI_>=19 have mostly -1<~[X/H]<~0 at z<~1. The metal-enriched gas probed by pLLSs and LLSs confirms that galaxies that have been enriching their CGM over billions of years. Surprisingly, despite this enrichment, there is also abundant metal-poor CGM gas (41%-59% of the pLLSs have [X/H]<~-1.4), representing a reservoir of near-pristine gas around z<~1 galaxies. We compare our empirical results to recent cosmological zoom simulations, finding some discrepancies, including an overabundance of metal- enriched CGM gas in simulations.