The decay of orthopositronium into three photons produces a physical realiz
ation of a pure state with three-party entanglement. Its quantum correlatio
ns an analyzed using recent results on quantum information theory, looking
for the final state that has the maximal amount of Greenberger, Home, and Z
eilinger like correlations. This state allows for a statistical dismissal o
f local realism stronger than the one obtained using any entangled state of
two spin one-half particles.