Settlement on decentralized ledgers enables flash loans --- loans that are both originated and repaid within the same instant of settlement time. We document empirically that these are used primarily for arbitrage. The settlement also allows settlement agents to expropriate profitable arbitrage trades. We show theoretically and empirically that private settlement emerges endogenously as a mechanism to mitigate this expropriation. We document payments from arbitrageurs to private settlers that exceed 1 million USD per day. In a simple model, we characterize the socially optimal mix of private and public settlement.