We have determined the quadratic slope parameter α for η→3π0 to be α = -0.031(4) from a 99% pure sample of 106η→3π0 decays produced in the reaction π-p→nη close to the η 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.