The CLAS detector was used to obtain the first ever measurement of the electromagnetic decay of the Σ*+(1385) from the reaction γp→K0Σ*+(1385). A real photon beam with a maximum energy of 3.8 GeV was incident on a liquid-hydrogen target, resulting in the photoproduction of the kaon and Σ+ hyperon. Kinematic fitting was used to separate the reaction channel from the background processes. The fitting algorithm exploited a new method to kinematically fit neutrons in the CLAS detector, leading to the measured decay widths ratio Σ+(1385)→Σ+γ/Σ+(1385)→Σ+π0=11.95±2.21(stat)+0.53−1.21(sys)% and a deduced partial width of 250.0±56.9(stat)+34.3−41.2(sys)  keV. A U-spin symmetry test using the SU(3) flavor-multiplet representation yields predictions for the Σ*+(1385)→Σ+γ and Σ*0(1385)→Λγ partial widths that agree with the experimental measurements.