Hedonic prices of locational attributes in urban land markets are determined by a process of spatial arbitrage that is similar to that which underpins the law of one price. If hedonic prices deviate from their spatial equilibrium values then individuals can benefit from changing locations. I examine whether the law holds for the hedonic price of rail access using a unique historical dataset for Berlin over the period 1890–1914, characterised by massive investment in the transport infrastructure. I estimate the hedonic price of rail access across multiple urban neighbourhoods and time periods to generate a panel dataset of hedonic price differences that I test for stationarity using a panel unit root test. Across multiple specifications I consistently fail to reject the null hypothesis of no unit root and accept the alternative hypothesis that the law holds. My estimates indicate a half-life for convergence to the law of one price that lies between 0.28 and 1.14 years. This result is consistent with spatial equilibrium.