A recently developed non-perturbative chiral approach to dynamically generate the 3/2 − baryon resonances has been extended to investigate the radiative decays Λ * (1520) → γΛ(1116) and Λ * (1520) → γΣ 0 (1193). We show that the Λ * (1520) decay into γΛ is an ideal test for the need of extra components of the resonance beyond those provided by the chiral approach since the largest meson-baryon components give no contribution to this decay. The case is different for γΣ decay where the theory agrees with experiment, though the large uncertainties of these data call for more precise measurements.