This paper formally derives an efficient estimator of the bid-ask spread from open, high, low, and close prices. The estimator is asymptotically unbiased and optimally combines the full set of price data to minimize the estimation variance. In absence of quote data, it delivers the most accurate estimates of bid-ask spreads theoretically, numerically, and empirically. The estimator is easy to calculate and has a broad applicability in empirical finance. We discuss implications for applied research.