We use extreme-value theory to estimate the ultimate world records for the 100-m running, for both men and women. For this aim we collected the fastest personal best times set between January 1991 and June 2008. Estimators of the extreme-value index are based on a certain number of upper order statistics. To optimize this number of order statistics we minimize the asymptotic mean-squared error of the moment estimator. Using the thus obtained estimate for the extremevalue index, the right endpoint of the speed distribution is estimated. The corresponding time can be interpreted as the estimated ultimate world record: the best possible time that could be run in the near future. We find 9.51 seconds for the 100-m men and 10.33 seconds for the women.