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We have determined the quadratic slope parameter alpha for eta-->3pi(0) to be alpha = -0.031(4) from a 99% pure sample of 10(6)eta-->3pi(0) decays produced in the reaction pi(-)p-->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.