The longitudinal target-spin asymmetry A_UL for the exclusive electroproduction of high energy photons was measured for the first time in p(e,e'p\gamma). The data have been accumulated at Jefferson Lab with the CLAS spectrometer using 5.7 GeV electrons and a longitudinally polarized NH_3 target. A significant azimuthal angular dependence was observed, resulting from the interference of the Deeply Virtual Compton Scattering and Bethe-Heitler processes. The amplitude of the sin(phi) moment is 0.252 +/- 0.042(stat) +/- 0.020(sys). Theoretical calculations are in good agreement with the magnitude and the kinematic dependence of the target-spin asymmetry, which is sensitive to the generalized parton distributions H and H-tilde.