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Cold accretion is a primary growth mechanism of simulated galaxies, yetobservational evidence of "cold flows" at redshifts where they should be mostefficient ($z=2$-4) is scarce. In simulations, cold streams manifest asLyman-limit absorption systems (LLSs) with low heavy-element abundances similarto those of the diffuse IGM. Here we report on an abundance survey of 17 HI-selected LLSs at $z=3.2$-4.4 which exhibit no metal absorption in SDSSspectra. Using medium-resolution spectra obtained at Magellan, we deriveionization-corrected metallicities (or limits) with a Markov-Chain Monte Carlosampling that accounts for the large uncertainty in $N_{\rm HI}$ measurementstypical of LLSs. The metal-poor LLS sample overlaps with the IGM in metallicityand is best described by a model where $71^{+13}_{-11}\%$ are drawn from theIGM chemical abundance distribution. These represent roughly half of all LLSsat these redshifts, suggesting that 28-40$\%$ of the general LLS population at$z\sim3.7$ could trace unprocessed gas. An ancillary sample of ten LLSs withoutany a priori metal-line selection is best fit with $48^{+14}_{-12}\%$ ofmetallicities drawn from the IGM. We compare these results with regions of amoving-mesh simulation; the simulation finds only half as many baryons inIGM-metallicity LLSs, and most of these lie beyond the virial radius of thenearest galaxy halo. A statistically significant fraction of all LLSs have lowmetallicity and therefore represent candidates for accreting gas; large-volumesimulations can establish what fraction of these candidates actually lie neargalaxies and the observational prospects for detecting the presumed hosts inemission.

The Incidence of Low-Metallicity Lyman-Limit Systems at z~3.5: Implications for the Cold-Flow Hypothesis of Baryonic Accretion