The neutron-induced fission cross-section of 233U has been measured at the CERN n TOF facility relative to the standard fission cross-section of 235U between 0.5 and 20MeV. The experiment was performed with a fast ionization chamber for the detection of the fission fragments and to discriminate against α-particles from the natural radioactivity of the samples. The high instantaneous flux and the low background of the n TOF facility result in data with uncertainties of ≈ 3%, which were found in good agreement with previous experiments. The high quality of the present results allows to improve the evaluation of the 233U(n,f) cross-section and, consequently, the design of energy systems based on the Th/U cycle.