  We calculate the chiral corrections to Weinberg's prediction for the S--wave
$\pi N$ scattering lengths up--to--and--including order ${\cal O}(M_\pi^3)$
making use of heavy baryon chiral perturbation theory. For the isospin--odd
scattering length $a^-$ these corrections are small and bring the prediction
closer to the empirical value. In the case of the isospin--even $a^+$ large
cancellations appear so that the ${\cal O}(M_\pi^3)$ result depends sensitively
on certain resonance parameters which enter the calculation of the contact
terms present at next--to--leading order.
