This paper re-examines the evidence on Purchasing Power Parity (PPP) in the long run. Previous studies have generally been unable to reject the hypothesis that the real exchange rate follows a random walk. If true, this implies that PPP does not hold. In contrast, this paper casts serious doubt on this random walk hypothesis. The results follow from more powerful estimation techniques, applied in a multilateral framework. Deviations from PPP, while substantial in the short run, appear to take about three years to be reduced in half.