  A measurement of elastic deeply virtual Compton scattering gamma* p -> gamma
p using e^+ p and e^- p collision data recorded with the H1 detector at HERA is
presented. The analysed data sample corresponds to an integrated luminosity of
306 pb^-1, almost equally shared between both beam charges. The cross section
is measured as a function of the virtuality Q^2 of the exchanged photon and the
centre-of-mass energy W of the gamma* p system in the kinematic domain 6.5 <
Q^2 < 80 GeV^2, 30 < W < 140 GeV and |t| < 1 GeV^2, where t denotes the squared
momentum transfer at the proton vertex. The cross section is determined
differentially in t for different Q^2 and W values and exponential t-slope
parameters are derived. Using e^+ p and e^- p data samples, a beam charge
asymmetry is extracted for the first time in the low Bjorken x kinematic
domain. The observed asymmetry is attributed to the interference between
Bethe-Heitler and deeply virtual Compton scattering processes. Experimental
results are discussed in the context of two different models, one based on
generalised parton distributions and one based on the dipole approach.
