We analyze how stochastic latency in the transaction settlement process, as introduced by distributed ledger systems, affects price efficiency. The time-consuming settlement process exposes arbitrageurs to price risk and imposes limits to arbitrage. We derive boundaries to price efficiency imposed by stochastic latency and show that larger price differences are consistent with higher expected latency, higher uncertainty in latency, or higher volatility. We parametrize stochastic latency in the Bitcoin network and estimate boundaries for high-frequency orderbook data from several exchanges. Stochastic latency explains about 74% of observed price differences adjusted for transaction costs.