  We use high-resolution cosmological zoom-in simulations from the FIRE project
to make predictions for the covering fractions of neutral hydrogen around
galaxies at z=2-4. These simulations resolve the interstellar medium of
galaxies and explicitly implement a comprehensive set of stellar feedback
mechanisms. Our simulation sample consists of 16 main halos covering the mass
range M_h~10^9-6x10^12 Msun at z=2, including 12 halos in the mass range
M_h~10^11-10^12 Msun corresponding to Lyman break galaxies (LBGs). We process
our simulations with a ray tracing method to compute the ionization state of
the gas. Galactic winds increase the HI covering fractions in galaxy halos by
direct ejection of cool gas from galaxies and through interactions with gas
inflowing from the intergalactic medium. Our simulations predict HI covering
fractions for Lyman limit systems (LLSs) consistent with measurements around
z~2-2.5 LBGs; these covering fractions are a factor ~2 higher than our previous
calculations without galactic winds. The fractions of HI absorbers arising in
inflows and in outflows are on average ~50% but exhibit significant time
variability, ranging from ~10% to ~90%. For our most massive halos, we find a
factor ~3 deficit in the LLS covering fraction relative to what is measured
around quasars at z~2, suggesting that the presence of a quasar may affect the
properties of halo gas on ~100 kpc scales. The predicted covering fractions,
which decrease with time, peak at M_h~10^11-10^12 Msun, near the peak of the
star formation efficiency in dark matter halos. In our simulations, star
formation and galactic outflows are highly time dependent; HI covering
fractions are also time variable but less so because they represent averages
over large areas.
