  We present the calculation of the hyperon forward spin polarizability gamma0
using manifestly Lorentz covariant baryon chiral perturbation theory including
the intermediate contribution of the spin 3/2 states. As at the considered
order the extraction of gamma0 is a pure prediction of chiral perturbation
theory, the obtained values are a good test for this theory. After including
explicitly the decuplet states, our SU(2) results have a very good agreement
with the experimental data and we extend our framework to SU(3) to give
predictions to the hyperons' gamma0 values. Prominent are the Sigma^- and Xi^-
baryons as their photon transition to the decuplet is forbidden in SU(3)
symmetry and therefore they are not sensitive to the explicit inclusion of the
decuplet in the theory.
