  Recent calculations of $s$-wave pion production have severely underestimated
the accurately known $pp\rightarrow pp\pi^0$\ total cross section near
threshold. In these calculations, only the single-nucleon axial-charge operator
is considered. We have calculated, in addition to the one-body term, the
two-body contributions to this reaction that arise from the exchange of mesons.
We find that the inclusion of the scalar $\sigma$-meson exchange current (and
lesser contributions from other mesons) increases the cross section by about a
factor of five, and leads to excellent agreement with the data. The results are
neither very sensitive to changes in the distorting potential that generates
the $NN$ wave function, nor to different choices for the meson-nucleon form
factors. We argue that $pp\rightarrow pp\pi^0$\ data provide direct
experimental evidence for meson-exchange contributions to the axial current.
