The beam-spin asymmetry in hard electroproduction of photons has been measured. The data have been accumulated by the HERMES experiment at DESY using the HERA 27.6 GeV longitudinally polarized positron beam and an unpolarized hydrogen-gas target. The asymmetry in the azimuthal distribution of the produced photons in the angle phi relative to the lepton scattering plane was determined with respect to the helicity state of the incoming positron beam. The beam-spin analyzing power in the sin phi moment was measured to be -0.23 +/- 0.04(stat) +/- 0.03(syst) in the missing-mass range below 1.7 GeV. The observed asymmetry is attributed to the interference of the Bethe-Heitler and deeply virtual Compton scattering processes.