The quark wave-functions of the lower-lying excited-state hyperons Λ(1405), Λ(1385), and Λ(1520) are not well understood. For example, the Λ(1405) may not be a regular three-quark state but K¯N molecule. Several competing models have been proposed, but none have been convincingly eliminated. Measuring radiative decays provides a means of discriminating between the models. The radiative branching ratios are predicted to be small (∼1%), but the radiative widths vary by factors of 2--10 from model to model. The existing experimental data is sparse and inconsistent; moreover, the radiative decay of the Sigma(1385) has never been observed before (except for one event). These lower-lying excited-state hyperons were produced in a tagged photon-beam experiment in the CLAS detector at TJNAF in the reaction gammap → K+Y* for photon energies from threshold to 2.4 GeV. The radiative branching ratio for the Sigma0(1385) relative to the Sigma0(1385) → Sigmapi0 channel was measured to be 0.021 +/- 0.008+0.004-0.007 corresponding to a partial width of 640 +/- 270+130-220 keV.