Assessing tsunami hazards commonly relies on historical accounts of past inundations, but such chronicles may be biased by temporal gaps due to historical circumstances. As a possible example, the lack of reports of tsunami inundation from the 1737 south-central Chile earthquake has been attributed to either civil unrest or a small tsunami due to deep fault slip below land. Here we conduct sedimentological and diatom analyses of tidal marsh sediments within the 1737 rupture area and find evidence for a locally-sourced tsunami consistent in age with this event. The evidence is a laterally-extensive sand sheet coincident with abrupt, decimetric subsidence. Coupled dislocation-tsunami models place the causative fault slip mostly offshore rather than below land. Whether associated or not with the 1737 earthquake, our findings reduce the average recurrence interval of tsunami inundation derived from historical records alone, highlighting the importance of combining geological and historical records in tsunami hazard assessment.