  We report Hubble Space Telescope/Cosmic Origins Spectrograph observations of
the Ly$\alpha$ emission and interstellar absorption lines in a sample of ten
star-forming galaxies at $z\sim0.2$. 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 Ly$\alpha$
emission in all ten galaxies, and 9/10 show double-peaked line profiles
suggestive of low HI column density. We measure Ly$\alpha$/H$\alpha$ flux
ratios of 0.5-5.6, implying that 5% to 60% of Ly$\alpha$ photons escape the
galaxies. These data confirm previous findings that low-ionization metal
absorption (LIS) lines are weaker when Ly$\alpha$ escape fraction and
equivalent width are higher. However, contrary to previously favored
interpretations of this trend, increased Ly$\alpha$ output cannot be the result
of varying HI covering: the Lyman absorption lines (Ly$\beta$ and higher) show
a covering fraction near unity for gas with $N_{HI} \gtrsim 10^{16}$ cm$^{-2}$.
Moreover, we detect no correlation between Ly$\alpha$ escape and the outflow
velocity of the LIS lines, suggesting that kinematic effects do not explain the
range of Ly$\alpha$/H$\alpha$ flux ratios in these galaxies. In contrast, we
detect a strong anti-correlation between the Ly$\alpha$ escape fraction and the
velocity separation of the Ly$\alpha$ emission peaks, driven primarily by the
velocity of the blue peak. As this velocity separation is sensitive to HI
column density, we conclude that Ly$\alpha$ escape in these Green Peas is
likely regulated by the HI column density rather than outflow velocity or HI
covering fraction.
