There is presently a conflict between fossil- and molecular-based evolutionary time scales. Molecular approaches for dating the branches of the tree of life frequently lead to substantially deeper times of divergence than those inferred by paleontologists. The discrepancy between molecular and fossil estimates persists despite the booming growth of sequence data sets, which increasingly feeds the interpretation that molecular estimates are older than stratigraphic dates because of deficiencies in the fossil record. Here we show that molecular time estimates suffer from a methodological handicap, namely that they are asymmetrically bounded random variables, constrained by a nonelastic boundary at the lower end, but not at the higher end of the distribution. This introduces a bias toward an overestimation of time since divergence, which becomes greater as the length of the molecular sequence and the rate of evolution decrease.