Résumé : The 7Be + p elastic cross section has been measured at the Centre de Recherches du Cyclotron RIB facility at Louvain-la-Neuve in the c.m. energy region from 0.3 to 0.75 MeV by bombarding a proton-rich target with a radioactive 7Be beam. The recoil protons have been detected in the angular range θc.m. = 120.2° - 131.1° and θc.m. = 156.6° - 170.2° using the LEDA system. From a R-matrix analysis of the cross section data, we extract the energy and the width of the 1+ resonance. The scattering lengths a01 = 25 ± 9 fm (channel spin I = 1 and a02 = -7 ± 3 fm (channel spin I = 2) are deduced. Implications on the low energy S-factor of the 7Be(p,γ)8B reaction are discussed.