The concept of time is critical in evolutionary thought, but rarely has it been considered as an object of theoretical research by evolutionary biologists. Evolution is an organism's possibility of access to the future; in other words, evolutionary reward is paid out as increased time. Replicating entities are granted time, but for them, time only serves to allow replication and evolution, and to further expand the frontier of time. The present review discusses the possible influence of considering time not as a pure dimension (or an a priori intuitive condition of human experience) but as an object in itself. At least as a metaphor, time can be considered as a self-replicating entity rooted in physical (including biological) beings, with the result of producing dimensional time. Time self-replication forces beings to replicate, which, in turn, further sustains the replication of time. In that sense, time-replication may constitute the driving force, i.e., the basic engine, providing directional energy to the evolutionary process. The philosophical roots, caveats, and perspectives of this hypothesis are presented here. The metaphor of replicating-time plays with the possibility of viewing time not as a merely regulatory component of scientific inquiry but instead, as a real and creative constituent of nature and, for this reason, an object worthy of research in the natural sciences.