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.