We report the first observation of an azimuthal asymmetry in the hard electroproduction of real photons with respect to the charge of the incoming lepton beam. The asymmetry is attributed to the interference between the Bethe-Heitler process and the deeply-virtual Compton scattering process, which gives access to the latter at the amplitude level. This process appears to be the theoretically cleanest way to access generalized parton distributions. The data have been accumulated by the HERMES experiment at DESY, scattering the HERA 27.6 GeV electron/positron beam off an unpolarized hydrogen gas target.