  In the framework of heavy baryon chiral perturbation theory, we give thIn the
framework of heavy baryon chiral perturbation theory, we give the chiral
expansion for the $\pi N \to \pi \pi N$ threshold amplitudes $D_1$ and $D_2$ to
quadratic order in the pion mass. The theoretical results agree within one
standard deviation with the empirical values. We also derive a relation between
the two threshold amplitudes of the reaction $\pi N \to \pi \pi N$ and the $\pi
\pi$ S--wave scattering lengths, $a_0^0$ and $a_0^2$, respectively, to order
${\cal O}(M_\pi^2)$. We show that there are uncertainties mostly related to
resonance excitation which make an accurate determination of the $\pi \pi$
scattering length $a_0^0$ from the $\pi \pi N$ threshold amplitudes at present
very difficult. The situation is different in the $\pi \pi$ isospin two final
state. Here, the chiral series converges and one finds $a_0^2 = -0.031 \pm
0.007$ consistent with the one--loop chiral perturbation theory prediction.
