Leading non-analytic corrections to hyperon non-leptonic decay amplitudes are calculated in chiral perturbation theory. The success of the Lee-Sugawara relation for S-wave amplitudes is understood in the context of chiral perturbation theory since the chiral logarithmic correction to this relation is small. Although corrections to individual S-wave amplitudes are more sizeable, good agreement with experiment is achieved. P-wave amplitudes are not well-described by the one-loop chiral perturbation theory calculation because the tree-level SU(3) symmetric contribution to these amplitudes is significantly suppressed. This suppression causes SU(3)-violating chiral corrections to dominate the P-wave amplitudes, making an accurate computation of these amplitudes impossible in chiral perturbation theory. The large chiral correction to the P-wave amplitudes does not imply a breakdown of chiral perturbation theory.