A new distribution-free estimator Qp of the pth population quantile is formulated, where Qp is a linear combination of order statistics admitting a jackknife variance estimator having excellent properties. The small sample efficiency of Qp is studied under a variety of light and heavy-tailed symmetric and asymmetric distributions. For the distributions and values of p studied, Qp is generally substantially more efficient than the traditional estimator based on one or two order statistics.