The discovery(1-6) of giant planets orbiting nearby solar-type stars raises anew the question of how they formed. Two very different mechanisms have been proposed. Gravitational instability(7,8) is the process by which planets form directly from the gas in the accrection disk around the young star. The other alternative is core accretion(9,10), where rocky cores of about 10 Earth masses form, followed by the hydrodynamical accretion of gas. Here I show that these processes have very different astrometric signatures, and that it is observationally possible to distinguish between them. Planets that form through gravitational instabilities do so rapidly, so that within just a few hundred years of the onset of the instability the nascent planet is making the young stellar object wobble in its orbit. This can be seen in the youngest stellar objects, with ages as little as 0.1 Myr. If planets form by core accretion, an observable wobble will not be visible for 10-20 Myr. Observations of a suitable ensemble of optically visible young stellar objects (such as those in the Taurus molecular cloud) over a period of several decades should be able to determine which of the two processes is responsible for giant-planet formation.