We have performed the first direct search for orthopositronium decay into two photons in order to determine if this decay, forbidden by space-rotational invariance, is the cause of the reported discrepancy in the orthopositronium decay rate. A high-resolution measurement of the photon-energy spectrum by a germanium detector was used to discriminate the expected sharp peak of the two-photon decay from the broader peak of the pickoA annihilations. No evidence of such decay is observed, resulting

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... n an upper limit on the branching ratio of 3.5x10, a factor of 6 below the level that could explain the decay-rate discrepancy.