Individuals often respond differently to identical treatments, and characterizing such variability in treatment response is an important aim in the practice of personalized medicine. In the context of time-to-event data, we describe a fully non-parametric accelerated failure time model that can be used to investigate and quantify the extent of treatment effect differences across study participants. By utilizing additive regression trees and non-parametric modeling of the error distribution, our approach can automatically accommodate a potentially large number of patient-specific covariates while addressing covariate interactions and non-linearities. In addition, we outline how our approach can be used both to identify subgroups of patients that may receive substantial treatment benefit and to guide the development of individualized treatment rules. Finally, we illustrate our proposed methodology with data from a clinical trial examining the treatment of chronic heart failure.