A measurement of the electroproduction of photons off protons in the deeply inelastic regime was performed at Jefferson Lab using a nearly 6 GeV electron beam, a longitudinally polarized proton target, and the CEBAF Large Acceptance Spectrometer. Target-spin asymmetries for ep→e′p′γ events, which arise from the interference of the deeply virtual Compton scattering and the Bethe-Heitler processes, were extracted over the widest kinematics in Q2, xB, t, and ϕ, for 166 four-dimensional bins. In the framework of generalized parton distributions, at leading twist the t dependence of these asymmetries provides insight into the spatial distribution of the axial charge of the proton, which appears to be concentrated in its center. These results also bring important and necessary constraints for the existing parametrizations of chiral-even generalized parton distributions.