We report on the first measurement of exclusive single-photon muoproduction on the proton by COMPASS using 160GeV/c polarised μ+ and μ− beams of the CERN SPS impinging on a liquid hydrogen target. We determine the dependence of the average of the measured μ+ and μ− cross sections for deeply virtual Compton scattering on the squared four-momentum transfer t from the initial to the final proton. The slope B of the t-dependence is fitted with a single exponential function, which yields B=(4.3±0.6stat|sys−0.3+0.1)(GeV/c)−2. This result can be converted into a transverse extension of partons in the proton, 〈r⊥2〉=(0.58±0.04stat|sys−0.02+0.01±0.04model)fm. For this measurement, the average virtuality of the photon mediating the interaction is 〈Q2〉=1.8(GeV/c)2 and the average value of the Bjorken variable is 〈xBj〉=0.056. Keywords: Quantum chromodynamics, Deep inelastic scattering, Exclusive reactions, Deeply virtual Compton scattering, Generalized Parton Distributions, Proton size, COMPASS