TTP99-20 alpha^2 corrections to parapositronium decay

Two-loop QED corrections to the decay rate of parapositronium (p-Ps) into two photons are presented. We find Gamma(p-Ps –> 2 photons) = 7989.50(2)/microsec. The non-logarithmic O(alpha^2) corrections turn out to be small, contrary to some earlier estimates. We speculate that the so-called ``orthopositronium lifetime puzzle'' will not likely be solved by large QED corrections.