  We calculate the noise induced in the anisotropies of the astrophysical
gravitational-wave background by finite sampling of both the galaxy
distribution and the compact binary coalescence event rate. This shot noise
leads to a scale-invariant bias term in the angular power spectrum $C_\ell$,
for which we derive a simple analytical expression. We find that this bias
dominates over the true cosmological power spectrum in any reasonable observing
scenario, and that only with very long observing times and removal of a large
number of foreground sources can the true power spectrum be recovered.
