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Once the terrestrial planets had mostly completed their assembly, bombardment continued by planetesimals left over from accretion. Highly siderophile element (HSE) abundances in Mars' mantle imply that its late accretion supplement was 0.8wt %; Earth and the Moon obtained an additional 0.7wt % and 0.02wt %, respectively. The disproportionately high Earth/Moon accretion ratio is explicable by stochastic addition of a few remaining Ceres-sized bodies that preferentially targeted Earth. Here we show that Mars' late accretion budget also requires a colossal impact, a plausible visible remnant of which is the emispheric dichotomy. The addition of sufficient HSEs to the Martian mantle entails an impactor of at least 1200km in diameter to have struck Mars before similar to 4430Ma, by which time crust formation was well underway. Thus, the dichotomy could be one of the oldest geophysical features of the Martian crust. Ejected debris could be the source material for its satellites.