Resolving early silicate differentiation timescales is crucial for understanding the chemical evolution and thermal histories of terrestrial planets. Planetary-scale magma oceans are thought to have formed during early stages of differentiation, but the longevity of such magma oceans is poorly constrained. In Mars, the absence of vigorous convection and plate tectonics has limited the scale of compositional mixing within its interior, thus preserving the early stages of planetary differentiation. The SNC (Shergotty-Nakhla-Chassigny) meteorites from Mars retain 'memory' of these events. Here we apply the short-lived 146Sm-142Nd and the long-lived 147Sm-143Nd chronometers to a suite of shergottites to unravel the history of early silicate differentiation in Mars. Our data are best explained by progressive crystallization of a magma ocean with a duration of approximately 100 million years after core formation. This prolonged solidification requires the existence of a primitive thick atmosphere on Mars that reduces the cooling rate of the interior.