While we perceive events in our environment through multiple sensory systems, we nevertheless perceive all of these events as occupying a single unified timeline. Time, as we perceive it, is unified. I argue that existing accounts of the perceived unity of time fail. Instead, the perceived unity of time must be constructed by integrating our initially fragmented timekeeping capacities. However, existing accounts of multimodal integration do not tell us how this might occur. Something new is needed. I finish the paper (...) by articulating the hurdles that must be overcome to provide an account of the perceived unity of time. (shrink)