The differential cross section dσ/dt for elastic ρ0 photoproduction, γp → ρ0ρ (ρ0 → π+π-), has been measured in ep interactions at HERA. The squared four-momentum exchanged at the proton vertex, t, has been determined directly by measuring the momentum of the scattered proton using the ZEUS Leading Proton Spectrometer (LPS), a large scale system of silicon micro-strip detectors operating close to the HERA proton beam. The LPS allows the measurement of the momentum of high energy protons scattered at small angles with accuracies of 0.4% for the longitudinal momentum and 5 MeV for the transverse momentum. Photoproduction of ρ0 mesons has been investigated in the interval 0.073 < |t| < 0.40 GeV2, for photon virtualities Q2 < 1 GeV2 and photon-proton centre-of-mass energies W between 50 and 100 GeV. In the measured range, the t distribution exhibits an exponential shape with a slope parameter b = 9.8 ± 0.8 (stat.) ± 1.1 (syst.) GeV-2. The use of the LPS eliminates the contamination from events with diffractive dissociation of the proton into low mass states. © Springler-Verlag 1997.