17O(p,p)17O elastic scattering cross sections were measured for the first time, on the INSP SAFIR platform in Paris, using thin silica films prepared by thermal oxidation of Si under 17O2. The 17O content of the film was determined by a combination of ellipsometry and IBA measurements. The yield of elastically scattered protons was determined from the corresponding peak in the Elastic Backscattering spectra, with the underlying Si signal reduced by channeling of the incident beam in the silicon substrate. The measured 17O(p,p)17O cross section was determined with a systematic uncertainty of about 14%. The cross section consists of resonant structures superimposed on a smoothly varying component that increases from about 1.2 times the Rutherford cross section at 600 keV to about 3 times Rutherford at 2 MeV. A resonance at 1230 keV shows promise for proton Elastic Backscattering depth profiling, especially at large backscattering angles. The cross section is available on IBANDL (www-nds.iaea.org/ibandl/)