  We compute the expected angular power spectrum of the cosmic Far Infrared
Background (FIRB). We find that the signal due to source correlations dominates
the shot--noise for $\ell \la 1000$ and results in anisotropies with rms
amplitudes $(\sqrt{\ell(\ell+1)C_\ell/2\pi})$ between 5% and 10% of the mean
for $l \ga 150$. The angular power spectrum depends on several unknown
quantities, such as the UV flux density evolution, optical properties of the
dust, biasing of the sources of the FIRB, and cosmological parameters. However,
when we require our models to reproduce the observed DC level of the FIRB, we
find that the anisotropy is at least a few percent in all cases. This
anisotropy is detectable with proposed instruments, and its measurement will
provide strong constraints on models of galaxy evolution and large-scale
structure at redshifts up to at least $z \sim5$.
