A magnitude 7.5 earthquake hit the city of Palu in Sulawesi, Indonesia on 28 September 2018 at 10:02:43 (coordinated universal time). It was followed a few minutes later by a 4-7-m-high tsunami. Palu is situated in a narrow pull-apart basin surrounded by high mountains of up to 2,000 m altitude. This morphology has been created by a releasing bend in the Palu-Koro fault, a rapidly moving left-lateral strike-slip fault. Here we present observations derived from optical and radar satellite imagery that constrain the ground surface displacements associated with the earthquake in great detail. Mapping of the main rupture and associated secondary structures shows that the slip initiated on a structurally complex and previously unknown fault to the north, extended southwards over 180 km and passed through two major releasing bends. The 30 km section of the rupture south of Palu city is extremely linear, and slightly offset from the mapped geological fault at the surface. This part of the rupture accommodates a large and smooth surface slip of 4-7 m, with no shallow slip deficit. Almost no aftershock seismicity was recorded from this section of the fault. As these characteristics are similar to those from known supershear segments, we conclude that the Palu earthquake probably ruptured this segment at supershear velocities.