We study the dynamics of price indices for major U.S. cities using panel econometric methods and find that relative price levels among cities mean revert at an exceptionally slow rate. In a panel of 19 cities from 1918 to 1995, we estimate the half-life of convergence to be approximately 9 years. These estimates provide an upper bound on speed of convergence that participants in European Monetary Union are likely to experience. The surprisingly slow rate of convergence can be explained by a combination of the presence of transportation costs, differential speeds of adjustment to small and large shocks, and the inclusion of non-traded goods prices in the overall price index.