A kernel estimator (KQ) of the quantile function is presented here. Boundary kernels are used for extrapolation of tail quantiles. The bandwidth of the estimator is chosen using an automatic, ''plug-in'' method. Confidence intervals for the estimated quantile are estimated by bootstrapping. Comparisons of the estimator with selected tail probability estimators are offered. The KQ estimator presented here is shown to be competitive with other estimators. ¿ American Geophysical Union 1994