Chiral prediction for the π<i>N</i><i>S</i>-wave scattering length<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">a</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">−</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>to order O(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="italic">M</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">π</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>)

We evaluate the S-wave pion-nucleon scattering length ${\mathit{a}}^{\mathrm{\ensuremath{-}}}$ in the framework of heavy baryon chiral perturbation theory up-to-and-including terms of order ${\mathit{M}}_{\mathrm{\ensuremath{\pi}}}^{4}$. We show that the order ${\mathit{M}}_{\mathrm{\ensuremath{\pi}}}^{4}$ piece of the isovector amplitude at threshold, ${\mathit{T}}_{\mathrm{thr}}^{\mathrm{\ensuremath{-}}}$, vanishes exactly. We predict for the isovector scattering length, 0.088${\mathit{M}}_{{\mathrm{\ensuremath{\pi}}}^{+}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\le}${\mathit{a}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\le}0.096${\mathit{M}}_{{\mathrm{\ensuremath{\pi}}}^{+}}^{\mathrm{\ensuremath{-}}1}$.

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