The Mw 7.8 Ecuador earthquake on 16 April 2016 is the sixth earthquake larger than Mw 7 to rupture the subduction megathrust between the Nazca and South American plates since the Mw 8.8 Colombia–Ecuador earthquake in 1906. We use Interferometric Synthetic Aperture Radar (InSAR) images from Sentinel‐1A to determine coseismic surface displacements associated with this earthquake. The interferograms exhibit a relatively simple pattern of deformation, with maximum displacements of 0.7 and 0.3 m on the descending and ascending images, respectively. We invert the interferograms for both rupture geometry and slip distribution in the earthquake. We find that the data are best described by slip on a fault dipping 17° to the east and that these InSAR data cannot uniquely constrain the strike. The maximum inferred slip is just over 2.5 m at about 20 km depth, with the main slip in the depth range of about 10–25 km. The geodetic moment of our preferred slip model is 7.15×1020 N·m, equivalent to Mw 7.87. Our results suggest that there is little, if any, partitioning of the oblique plate convergence. The 2016 Ecuador earthquake is coincident with the location of the 1942 Mw 7.8 earthquake, with both earthquakes most likely rupturing an asperity that also failed in the 1906 Mw 8.8 earthquake.