A measurement is presented of elastic deeply virtual Compton scattering 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 p system, W, and for the first time, differentially in the squared momentum transfer at the proton vertex, t, in the kinematic range , and . QCD based calculations at next-to-leading order using generalized parton distributions can describe the data, as can colour dipole model predictions.