We report the first determination of the upper limit for the branching ratio
of the CP forbidden decay eta to 4 pi0. No events were observed in a sample
of 3.0×10^7 eta decays. The experiment was performed with the Crystal Ball
multiphoton spectrometer installed in a separated pi- beam at the AGS
(Alternating Gradient Synchrotron). At the 90% confidence limit,
B(eta to 4 pi0) ⇐ 6.9×10^-7.