We investigate the nonparametric estimation of Kendall's coefficient of concordance, ?, for measuring the association between two variables under bivariate censoring. The proposed estimator is a modification of the estimator introduced by Oakes (1982), using a Horvitz-Thompson-type correction for the pairs that are not orderable. With censored data, a pair is orderable if one can establish whether the uncensored pair is discordant or concordant using the data available for that pair. Our estimator is shown to be consistent and asymptotically normally distributed. A simulation study shows that the proposed estimator performs well when compared with competing alternatives. The various methods are illustrated with a real data set.