By analyzing the meaning of time I argue, without endorsing operationalism, that time is necessarily related to physical systems which can serve as clocks. This leads to a version of relationism about time which entails that there is no time 'before' the universe. Three notions of metaphysical 'time' (associated, respectively, with time as a mathematical concept, substantivalism, and modal relationism) which might support the idea of time 'before' the universe are discussed. I argue that there are no good reasons to (...) believe that metaphysical 'time' can be identified with what we ordinarily call time. I also briefly review and criticize the idea of time 'before' the big bang, associated with some recent speculative models in modern cosmology, and I argue that if the big bang model is a (roughly) correct description of our universe, then the best current answer to the question in the title is that time did have a beginning. (shrink)