The 16 June 1819 Rann of Kachchh earthquake was felt throughout much of India. Although significant vertical movements of the ground caused flooding of regions near sea level, damming of a distributary of the Indus river, widespread liquefaction, and a local tsunami, the geometry of the fault plane has hitherto remained obscure. Dislocation models based on deformation data gathered 7 and 25 years after the earthquake suggest that a near-surface reverse fault slipped locally more than 11 m, and that rupture extended at least 80 km along strike. Estimates of maximum uplift and depression during the earthquake yield similar, but not identical, solutions to those based solely on a levelling profile across the zone of uplift, known as the Allah Bund. The inferred 50-70~ fault plane beneath the Allah Bund is unfavourably steep for reverse faulting, and its down-dip width (6-10 km) short for slip exceeding 10 m. Some forms oflistric fault geometry are also consistent with the observed surface deformation fields, with increased fault width (15-25km) and similar coseismic slip. A geometric moment magnitude of M = 7.7 + 0.2 is obtained from the inferred slip parameters, assuming uniform along-strike slip, consistent with a magnitude estimated empirically from the intensity distribution. Although a recurrence of the Kachchh earthquake is unlikely soon because of low inferred contractional strain rates in the region, the westward continuation of the Kachchh rift zone could host future ruptures contiguous with the 1819 event, with important consequences for the city of Karachi.