The longitudinal target-spin asymmetry ${A}_{\mathrm{UL}}$ for the exclusive electroproduction of high-energy photons was measured for the first time in $e\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\rightarrow}{e}^{\ensuremath{'}}p\ensuremath{\gamma}$. The data have been accumulated at JLab with the CLAS spectrometer using 5.7 GeV electrons and a longitudinally polarized ${\mathrm{NH}}_{3}$ 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 $\mathrm{sin}\ensuremath{\phi}$ moment is $0.252\ifmmode\pm\else\textpm\fi{}{0.042}^{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.020}^{\mathrm{sys}}$. 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 $\stackrel{\texttildelow{}}{H}$ and $H$.