Late-onset (LO) toxicities are a serious concern in many phase I trials. Since most dose-limiting toxicities occur soon after therapy begins, most dose-finding methods use a binary indicator of toxicity occurring within a short initial time period. If an agent causes LO toxicities, however, an undesirably large number of patients may be treated at toxic doses before any toxicities are observed. A method addressing this problem is the time-to-event continual reassessment method (TITE-CRM, Cheung and Chappell, 2000). We propose a Bayesian dose-finding method similar to the TITE-CRM in which doses are chosen using time-to-toxicity data. The new aspect of our method is a set of rules, based on predictive probabilities, that temporarily suspend accrual if the risk of toxicity at prospective doses for future patients is unacceptably high. If additional follow-up data reduce the predicted risk of toxicity to an acceptable level, then accrual is restarted, and this process may be repeated several times during the trial. A simulation study shows that the proposed method provides a greater degree of safety than the TITE-CRM, while still reliably choosing the preferred dose. This advantage increases with accrual rate, but the price of this additional safety is that the trial takes longer to complete on average.