The explicit breaking of the axial symmetry by quantum fluctuations gives rise to the so-called axial anomaly. This phenomenon is solely responsible for the decay of the neutral pion pi(0) into two photons (gamma gamma), leading to its unusually short lifetime. We precisely measured the decay width Gamma of the pi(0) -> gamma gamma process. The differential cross sections for pi(0) photoproduction at forward angles were measured on two targets, carbon-12 and silicon-28, yielding Gamma( pi(0) -> gamma gamma) = 7.798 +/- 0.056(stat.) +/- 0.109(syst) eV, where stat. denotes the statistical uncertainty and syst. the systematic uncertainty. We combined the results of this and an earlier experiment to generate a weighted average of Gamma( pi(0) -> gamma gamma) = 7.802 +/- 0.052(stat.) t 0.105(syst) eV. Our final result has a total uncertainty of 1.50% and confirms the prediction based on the chiral anomaly in quantum chromodynamics.