We have determined the quadratic slope parameter alpha for eta to 3 pi0
to be alpha = -0.031(4) from a 99% pure sample of 10^6 eta to 3 pi0 decays
produced in the reaction pi- p to n eta close to the eta threshold
using the Crystal Ball detector at the AGS. The result is four times
more precise than the present world data and disagrees with current
chiral perturbation theory calculations by about four standard deviations.