A Comment on the Radiative Decays of the $\Lambda (1405)$

We examine the radiative decays of the Lambda (1405) to octet baryons, Lambda + gamma and Sigma + gamma. In the limit of SU(3) symmetry the decay rates for these two modes are related, and we compute the leading correction to the relation in chiral perturbation theory. Such measurements will allow the sign of the strong coupling $g_{\Lambda^*}$ to be determined. The SU(3) violating radiative decay to the baryon decuplet Sigma* + gamma dominated by one-loop graphs is also discussed. Experiments planned for the Jefferson Laboratory should be able to measure some, if not all, of the processes considered.