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The 2018 magnitude 7.5 Palu, Indonesia, earthquake, which triggered liquefaction, landslides and a tsunami, was one of the most devastating earthquakes of 2018. The speed at which an earthquake rupture propagates affects its energy balance and ground shaking impact. Dynamic models of supershear earthquakes, which are faster than the speed of shear waves, often start at subshear speed and later run faster than Eshelby’s speed. Here we present robust evidence of an early and persistent supershear rupture at the sub-Eshelby speed of the 2018 magnitude 7.5 Palu, Indonesia, earthquake. Slowness-enhanced back-projection of teleseismic data provides a sharp image of the rupture process, along a path consistent with the surface rupture trace inferred by subpixel correlation of synthetic-aperture radar and satellite optical images. The rupture propagated at a sustained velocity of 4.1 km s–1 from its initiation to its end, despite large fault bends. The persistent supershear speed is further validated by seismological evidence of far-field Rayleigh Mach waves. The unusual features of this earthquake probe the connections between the rupture dynamics and fault structure. They may also offer a clue to understand why this earthquake was so damaging: did supershear rupture cause a cascade of effects, by inducing submarine landslides which in turn contributed to the tsunami?