  A measurement is presented of elastic deeply virtual Compton scattering
\gamma* p \to \gamma p made using e^+ p collision data corresponding to a
luminosity of 46.5 pb^{-1}, taken with the H1 detector at HERA. The cross
section is measured as a function of the photon virtuality, Q^2, the invariant
mass of the \gamma* p system, W, and for the first time, differentially in the
squared momentum transfer at the proton vertex, t, in the kinematic range 2 <
Q^2 < 80 GeV^2, 30 < W < 140 GeV and |t| < 1 GeV^2. QCD based calculations at
next-to-leading order using generalized parton distributions can describe the
data, as can colour dipole model predictions.
