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We use a large sample of galaxies at z~3 to establish a relationship betweenreddening, neutral gas covering fraction (fcov(HI)), and the escape of ionizingphotons at high redshift. Our sample includes 933 galaxies at z~3, 121 of whichhave very deep spectroscopic observations (>7 hrs) in the rest-UV(lambda=850-1300 A) with Keck/LRIS. Based on the high covering fraction ofoutflowing optically-thick HI indicated by the composite spectra of thesegalaxies, we conclude that photoelectric absorption, rather than dustattenuation, dominates the depletion of ionizing photons. By modeling thecomposite spectra as the combination of an unattenuated stellar spectrumincluding nebular continuum emission with one that is absorbed by HI andreddened by a line-of-sight extinction, we derive an empirical relationshipbetween E(B-V) and fcov(HI). Galaxies with redder UV continua have largercovering fractions of HI characterized by higher line-of-sight extinctions. Ourresults are consistent with the escape of Lya through gas-free lines-of-sight.Covering fractions based on low-ionization interstellar absorption linessystematically underpredict those deduced from the HI lines, suggesting thatmuch of the outflowing gas may be metal-poor. We develop a model which connectsthe ionizing escape fraction with E(B-V), and which may be used to estimate theescape fraction for an ensemble of high-redshift galaxies. Alternatively,direct measurements of the escape fraction for our data allow us to constrainthe intrinsic 900-to-1500 A flux density ratio to be >0.20, a value that favorsstellar population models that include weaker stellar winds, a flatter initialmass function, and/or binary evolution. Lastly, we demonstrate how theframework discussed here may be used to assess the pathways by which ionizingradiation escapes from high-redshift galaxies. [Abridged]

The Connection Between Reddening, Gas Covering Fraction, and the Escape of Ionizing Radiation at High Redshift