  The matrix element for the decay of orthopositronium to three photons can be
expressed in terms of three independent amplitudes. We describe the analytic
evaluation of these amplitudes, both to lowest order and with the inclusion of
all one-loop corrections. We use these amplitudes to find precise values for
the one-loop correction to the orthopositronium decay rate
Gamma_1=-10.286606(10) (alpha/pi) Gamma_{LO}, and for the order-alpha^2
"square" correction to the decay rate Gamma_2(square) = 28.860(2) (alpha/pi)^2
Gamma_{LO}, where Gamma_{LO} is the lowest order rate. We give in explicit form
the function describing the one-loop correction to the distribution in phase
space of the final state photons.
