  The one-loop functional for chiral SU(2) of Gasser and Leutwyler is extended
to include up to three propagators. With this generating functional it is
possible to calculated all amplitudes up to order phi^6 to next-to-leading
order in the low-energy expansion. An external pion is of order phi and a
vector gauge boson is of order phi^2. A check of the existing amplitudes for
two photons into two pions is given. The one-loop amplitudes and the cross
sections for four-pion production in e^+e^- annihilation are calculated.
