  A measurement is presented of elastic Deeply Virtual Compton Scattering e^+ +
p -> e^+ + photon + p at HERA using data taken with the H1 detector. The cross
section is measured as a function of the photon virtuality, Q^2, and the
invariant mass, W, of the gamma p system, in the kinematic range 2 < Q^2 < 20
GeV^2, 30 < W < 120 GeV and |t| < 1 GeV^2, where t is the squared momentum
transfer to the proton. The measurement is compared to QCD based calculations.
