  We present results from the Keck Baryonic Structure Survey (KBSS), a unique
spectroscopic survey designed to explore the connection between galaxies and
intergalactic baryons. The KBSS is optimized for the redshift range z ~ 2-3,
combining S/N ~ 100 Keck/HIRES spectra of 15 hyperluminous QSOs with densely
sampled galaxy redshift surveys surrounding each QSO sightline. We perform
Voigt profile decomposition of all 6000 HI absorbers within the full Lya forest
in the QSO spectra. Here we present the distribution, column density,
kinematics, and absorber line widths of HI surrounding 886 star-forming
galaxies with 2.0 < z < 2.8 and within 3 Mpc of a QSO sightline. We find that
N_HI and the multiplicity of HI components increase rapidly near galaxies. The
strongest HI absorbers within ~ 100 physical kpc of galaxies have N_HI ~ 3 dex
higher than those near random locations in the IGM. The circumgalactic zone of
most enhanced HI absorption (CGM) is found within 300 kpc and 300 km/s of
galaxies. Nearly half of absorbers with log(N_HI) > 15.5 are found within the
CGM of galaxies meeting our photometric selection, while their CGM occupy only
1.5% of the cosmic volume. The spatial covering fraction, multiplicity of
absorption components, and characteristic N_HI remain elevated to transverse
distances of 2 physical Mpc. Absorbers with log(N_HI) > 14.5 are tightly
correlated with the positions of galaxies, while absorbers with lower N_HI are
correlated only on Mpc scales. Redshift anisotropies on Mpc scales indicate
coherent infall toward galaxies, while on scales of ~100 physical kpc peculiar
velocities of 260 km/s are indicated. The median Doppler widths of absorbers
within 1-3 virial radii of galaxies are ~50% larger than randomly chosen
absorbers of the same N_HI, suggesting higher gas temperatures and/or increased
turbulence likely caused by accretion shocks and/or galactic winds.
