  The decay $\eta \to \pi^0 \gamma \gamma$ is discussed in the framework of
SU(3) chiral perturbation theory. The process is dominated by the
${\cal{O}}(p^6)$ in the momentum expansion where tree-level amplitudes from the
effective Lagrangian ${\cal{L}}^6$ enter together with one--loop contributions
from ${ \cal{L}}^4$ and two--loop contributions from ${\cal{L}}^2$. We estimate
the 6 independent ${\cal{L}}^6$ coupling constants by resonance saturation
consistent with the pion production process $\gamma \gamma \to \pi^0 \pi^0$ and
calculate the pion--loop part of the one- and two--loop amplitude. Predictions
for the total rate and spectrum of $\eta \to \pi^0 \gamma \gamma$ are given
together with a discussion of the uncertainties involved.
