We present a novel temporal illusion in which the perceived order of events is dictated by their perceived causal relationship. Participants view a simple Michotte-style launching sequence featuring 3 objects, in which one object starts moving before its presumed cause. Not only did participants re-order the events in a causally consistent way, thus violating the objective temporal order, but they also failed to recognise the clip they had seen, preferring a clip in which temporal and causal order matched. We show that the effect is not due to lack of attention to the presented events and we discuss the problem of determining whether causality affects temporal order at an early perceptual stage or whether it distorts an accurately perceived order during retrieval. Alternatively, we propose a mechanism by which temporal order is neither misperceived nor misremembered but inferred "on-demand" given phenomenal causality and the temporal priority principle, the assumption that causes precede their effects. Finally, we discuss how, contrary to theories of causal perception, impressions of causality can be generated from dynamic sequences with strong spatiotemporal deviations.