The use of an additional defining point on the International Temperature Scale between 90.188 K and 273.15 K is advocated. The triple point of xenon is suggested as the candidate and an experimental technique which gives the required degree of reproducibility for the melting curves is described. Results obtained for natural xenon and xenon enriched to 80% 136Xe are given. It is concluded that the triple point of xenon can be realized with sufficient reproducibility that it can be used as a defining point on an International Temperature Scale.