[en] A measurement of elastic deeply virtual Compton scattering γ^*p→γp 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 Q² of the exchanged photon and the centre-of-mass energy W of the γ^*p system in the kinematic domain 6.5 < Q² < 80 GeV², 30< W<140 GeV and vertical stroke t vertical stroke <1 GeV², where t denotes the squared momentum transfer at the proton vertex. The cross section is determined differentially in t for different Q² 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. (orig.)