We investigate the leading-order amplitudes for weak radiative decays of hyperons in chiral perturbation theory. We consistently include contributions from the next-to-leading order weak-interaction Lagrangian. It is shown that due to these terms Hara's theorem is violated. The data for the decay rates of the charged hyperons can be accounted for. However, at this order in the chiral expansion, the four decay rates of the neutral hyperons satisfy relations which are in disagreement with the data. The asymmetry parameters for all the decays cannot be accounted for without higher-order terms. We briefly comment on the effect of the 27-plet part of the weak interaction.