We report Hubble Space Telescope/Cosmic Origins Spectrograph observations of the Lyα emission and interstellar absorption lines in a sample of 10 star-forming galaxies at z ∼ 0.2. Selected on the basis of high equivalent width optical emission lines, the sample, dubbed "Green Peas," make some of the best analogs for young galaxies in an early universe. We detect Lyα emission in all ten galaxies, and 9/10 show double-peaked line profiles suggestive of low H i column density. We measure Lyα/Hα flux ratios of 0.5-5.6, implying that 5-60% of Lyα photons escape the galaxies. These data confirm previous findings that low-ionization metal absorption (LIS) lines are weaker when Lyα escape fraction and equivalent width are higher. However, contrary to previously favored interpretations of this trend, increased Lyα output cannot be the result of a varying H I covering: the Lyman absorption lines (Lyβ and higher) show a covering fraction near unity for gas with NH i ≳ 1016 cm-2. Moreover, we detect no correlation between Lyα escape and the outflow velocity of the LIS lines, suggesting that kinematic effects do not explain the range of Lyα/Hα flux ratios in these galaxies. In contrast, we detect a strong anticorrelation between the Lyα escape fraction and the velocity separation of the Lyα emission peaks, driven primarily by the velocity of the blue peak. As this velocity separation is sensitive to H I column density, we conclude that Lyα escape in these Green Peas is likely regulated by the H I column density rather than outflow velocity or H I covering fraction.Based on observations made with the NASA/ESA Hubble Space Telescope, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs 12928 and 11727.