|Abstract||The ability to date the time of divergence between lineages using molecular data provides the opportunity to answer many important questions in evolutionary biology. However, molecular dating techniques have previously been criticized for failing to adequately account for variation in the rate of molecular evolution. We present a maximum-likelihood approach to estimating divergence times that deals explicitly with the problem of rate variation. This method has many advantages over previous approaches including the following: (1) a rate constancy test excludes data for which rate heterogeneity is detected; (2) date estimates are generated with confidence intervals that allow the explicit testing of hypotheses regarding divergence times; and (3) a range of sequences and fossil dates are used, removing the reliance on a single calculated calibration rate. We present tests of the accuracy of our method, which show it to be robust to the effects of some modes of rate variation. In addition, we test the effect of substitution model and length of sequence on the accuracy of the dating technique. We believe that the method presented here offers solutions to many of the problems facing molecular dating and provides a platform for future improvements to such analyses.