For safety and ethical reasons, a data monitoring committee of a clinical trial may wish to assess the futility of continuing a trial if the currently available data at an interim look show no beneficial effect due to treatment, especially when accompanied by mounting evidence of treatment emergent adverse effects. Stochastic curtailing whereby conditional power is evaluated given currently observed data is one way of evaluating futility. In clinical trials that look at "time-to-event" as the primary outcome, difference between treatment groups with respect to the primary outcome is commonly evaluated using the log-rank test. Although the unconditional power function for the log-rank test has been described previously, its conditional power has not been widely investigated. We describe a method for evaluating conditional power when the log-rank test is used to assess the difference between the survival distributions of two treatment groups with respect to some failure-time outcome. The method is useful under a wide range of assumptions regarding the underlying survival distribution, patient entry distribution, losses to follow-up, and (if applicable) noncompliance, drop-ins, lag in treatment effect, and stratification. This level of applicability is attained by generalizing a flexible Markov chain approach to unconditional power computation, described previously, to compute conditional power.