The reaction gamma p -> p pi0 gamma has been measured with the Crystal Ball / TAPS detectors using the energy-tagged photon beam at the electron accelerator facility MAMI-B. Energy and angular differential cross sections for the emitted photon gamma and angular differential cross sections for the pi0 have been determined with high statistics in the energy range of the Delta+(1232) resonance. Cross sections and the ratio of the cross section to the non-radiative process gamma p -> p pi0 are compared to theoretical reaction models, having the anomalous magnetic moment kappa_Delta+ as free parameter. As the shape of the experimental distributions is not reproduced in detail by the model calculations, currently no extraction of kappa_Delta+ is feasible.