AbstractChen and Chaloner (Statist. Med. 2006; 25:2956–2966. DOI: 10.1002/sim.2429) present a Bayesian stopping rule for a single‐arm clinical trial with a binary endpoint. In some cases, earlier stopping may be possible by basing the stopping rule on the time to a binary event. We investigate the feasibility of computing exact, Bayesian, decision‐theoretic time‐to‐event stopping rules for a single‐arm group sequential non‐inferiority trial relative to an objective performance criterion. For a conjugate prior distribution, exponential failure time distribution, and linear and threshold loss structures, we obtain the optimal Bayes stopping rule by backward induction. We compute frequentist operating characteristics of including Type I error, statistical power, and expected run length. We also briefly address design issues. Copyright © 2009 John Wiley & Sons, Ltd.