  The fraction of ionizing photons that escape from young star-forming galaxies
is one of the largest uncertainties in determining the role of galaxies in
cosmic reionization. Yet traditional techniques for measuring this fraction are
inapplicable at the redshifts of interest due to foreground screening by the
Lyman alpha forest. In an earlier study, we demonstrated a reduction in the
equivalent width of low-ionization absorption lines in composite spectra of
Lyman break galaxies at z=4 compared to similar measures at z=3. This might
imply a lower covering fraction of neutral gas and hence an increase with
redshift in the escape fraction of ionizing photons. However, our spectral
resolution was inadequate to differentiate between several alternative
explanations, including changes with redshift in the outflow kinematics. Here
we present higher quality spectra of 3 gravitationally lensed Lyman break
galaxies at z=4 with a spectral resolution sufficient to break this degeneracy
of interpretation. We present a method for deriving the covering fraction of
low-ionization gas as a function of outflow velocity and compare the results
with similar quality data taken for galaxies at lower redshift. We find a
significant trend of lower covering fractions of low-ionization gas for
galaxies with strong \Lya emission. In combination with the demographic trends
of \Lya emission with redshift from our earlier work, our results provide new
evidence for a reduction in the average H I covering fraction, and hence an
increase in the escape fraction of ionizing radiation from Lyman break
galaxies, with redshift.
