We study in QCD the physics of deeply virtual Compton scattering (DVCS
)-the virtual Compton process in the large s and small t kinematic reg
ion. We show that DVCS can probe a new type of off-forward parton dist
ributions. We derive an Altarelli-Parisi-type of evolution equations f
or these distributions. We also derive their sum rules in terms of nuc
leon form factors of the twist-two quark and gluon operators. In parti
cular, we find that the second sum rule is related to fractions of the
nucleon spin carried separately by quarks and gluons. We estimate the
cross section for DVCS and compare it with the accompanying Bethe-Hei
tler process at CEBAF and HERMES kinematics.