  The feasibility for a measurement of the exclusive production of a real
photon, a process although known as Deeply Virtual Compton Scattering (DVCS) at
an Electron Ion Collider (EIC) has been explored. DVCS is universally believed
to be a golden measurement toward the determination of the Generalized Parton
Distribution (GPDs) functions. The high luminosity of the machine, expected in
the order of 10^34 cm^-2 s^-1 at the highest center-of-mass energy, together
with the large resolution and rapidity acceptance of a newly designed dedicated
detector, will open a opportunity for very high precision measurements of DVCS,
and thus for the determination of GPDs, providing an important tool toward a
2+1 dimensional picture of the internal structure of the proton and nuclei.
