This paper summarises the measuring procedures and the results of the tritium accounting during the first Tritium Experiment at JET, carried out in November 1991. The measurement of the amount of tritium injected into the Torus and of the quantity recovered from the Torus and the Neutral Injector Boxes is described and the accuracy of the data assessed. The new Gas Collection System used during the experiment is briefly described. The tritium recovery data taken in the months following the experiment are reviewed, with special attention to the first three weeks after the experiment. The total amount of tritium collected in the Gas Collection System is compared with the data of tritium release from the Torus and the Neutral Injection Boxes. The analysis of the data allows us to estimate the residual tritium inventory in the Injection System and in the Torus.