We present a method to estimate the gains from trade in limit-order markets and provide empirical evidence that the limit-order market is a good market design. Using observations on order submissions and execution and cancellation histories, we estimate both the distribution of traders' unobserved valuations for the stock and latent trader arrival rates. We use the resulting estimates to compute the current gains from trade, the gains from trade in a perfectly liquid market, and the gains from trade with a monopoly liquidity supplier. The current gains are 90% of the maximum gains and 150% of the monopolist gains.