We develop and estimate an econometric model of limit-order execution times using survival analysis and actual limit-order data. We estimate versions for time-to-first-fill and time-to-completion for both buy and sell limit orders, and incorporate the effects of explanatory variables such as the limit price, limit size, bid/offer spread, and market volatility. Execution times are very sensitive to the limit price, but are not sensitive to limit size. Hypothetical limit-order executions, constructed either theoretically from first-passage times or empirically from transactions data, are very poor proxies for actual limit-order executions.