Initially, the devastating Mw 7.0, 12 January 2010 Haiti earthquake seemed to involve straightforward accommodation of oblique relative motion between the Caribbean and North American plates along the Enriquillo-Plantain Garden fault zone. Here, we combine seismological observations, geologic field data and space geodetic measurements to show that, instead, the rupture process may have involved slip on multiple faults. Primary surface deformation was driven by rupture on blind thrust faults with only minor, deep, lateral slip along or near the main Enriquillo-Plantain Garden fault zone; thus the event only partially relieved centuries of accumulated left-lateral strain on a small part of the plate-boundary system. Together with the predominance of shallow off-fault thrusting, the lack of surface deformation implies that remaining shallow shear strain will be released in future surface-rupturing earthquakes on the Enriquillo-Plantain Garden fault zone, as occurred in inferred Holocene and probable historic events. We suggest that the geological signature of this earthquake-broad warping and coastal deformation rather than surface rupture along the main fault zone-will not be easily recognized by standard palaeoseismic studies. We conclude that similarly complex earthquakes in tectonic environments that accommodate both translation and convergence-such as the San Andreas fault through the Transverse Ranges of California-may be missing from the prehistoric earthquake record.