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We develop a model of an order-driven exchange competing for order flow with off-exchange trading mechanisms. Liquidity suppliers face a trade-off between benefits and costs of order exposure. If they display trading intentions, they attract additional trade demand. We show, in equilibrium, hiding trade intentions can induce mis-coordination between liquidity supply and demand, generate excess price fluctuations and harm price efficiency. Econometric high-frequency analysis based on unique data on hidden orders from NASDAQ reveals strong empirical support for these predictions: We find abnormal reactions in prices and order flow after periods of high excess-supply of hidden liquidity.