  We investigate the rare radiative eta decay modes
$\eta\to\pi^+\pi^-\gamma\gamma$ and $\eta\to\pi^0\pi^0\gamma\gamma$ within the
framework of chiral perturbation theory at $O(p^4)$. We present photon spectra
and partial decay rates for both processes as well as a Dalitz contour plot for
the charged decay.
