We present the calculation of the hyperon forward spin polarizability γ0 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 γ0 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 for the hyperons’ γ0 values. Prominent are the Σ− and Ξ− 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.