Eucrites are a group of meteorites that represent the first planetary igneous activity following metal-silicate differentiation on an early planetesimal, similar to Asteroid 4 Vesta, and, thus, help date geophysical processes occurring on such bodies in the early solar system. Using the short-lived radionuclide (182)Hf as a relative chronometer, we demonstrate that eucrite zircon crystallized quickly within 6.8 million years of metal-silicate differentiation. This implies that mantle differentiation on the eucrite parent body occurred during a period when internal heat from the decay of (26)Al and (60)Fe was still available. Later metamorphism of eucrites took place at least 8.9 million years after the zircons crystallized and was likely caused by heating from impacts, or by burial under hot material excavated by impacts, rather than from lava flows. Thus, the timing of eucrite formation and of mantle differentiation is constrained.