  The 40% Arecibo Legacy Fast ALFA (ALFALFA) survey catalog (\alpha.40) of
approximately 10,150 HI-selected galaxies is used to analyze the clustering
properties of gas-rich galaxies. By employing the Landy-Szalay estimator and a
full covariance analysis for the two-point galaxy-galaxy correlation function,
we obtain the real-space correlation function and model it as a power law,
\xi(r) = (r/r_0)^(-\gamma), on scales less than 10 h^{-1} Mpc. As the largest
sample of blindly HI-selected galaxies to date, \alpha.40 provides detailed
understanding of the clustering of this population. We find \gamma = 1.51 +/-
0.09 and r_0 = 3.3 +0.3, -0.2 h^{-1} Mpc, reinforcing the understanding that
gas-rich galaxies represent the most weakly clustered galaxy population known;
we also observe a departure from a pure power law shape at intermediate scales,
as predicted in \Lambda CDM halo occupation distribution models. Furthermore,
we measure the bias parameter for the \alpha.40 galaxy sample and find that HI
galaxies are severely antibiased on small scales, but only weakly antibiased on
large scales. The robust measurement of the correlation function for gas-rich
galaxies obtained via the \alpha.40 sample constrains models of the
distribution of HI in simulated galaxies, and will be employed to better
understand the role of gas in environmentally-dependent galaxy evolution.
