  We present a calculation of the fourth-order (NLO) contribution to
spin-dependent forward Compton scattering in heavy-baryon chiral perturbation
theory. No low-energy constants, except for the anomalous magnetic moments of
the nucleon, enter at this order. The fourth-order piece of the spin
polarisability of the proton turns out to be almost twice the size of the
leading piece, with the opposite sign. This leads to the conclusion that no
prediction can currently be made for this quantity.
