We obtain a geometrical condition on vacuum, stationary,asymptotically flat spacetimes which is necessary and sufficientfor the spacetime to be locally isometric to Kerr. Namely, weprove a theorem stating that an asymptotically flat, stationary,vacuum spacetime such that the so-called Killing form is aneigenvector of the self-dual Weyl tensor must be locallyisometric to Kerr. Asymptotic flatness is a fundamentalhypothesis of the theorem, as we demonstrate by writing down thefamily of metrics obtained when this requirement is dropped.This result indicates why the Kerr metric plays such animportant role in general relativity. It may also be ofinterest in order to extend the uniqueness theorems of blackholes to the non-connected and to the non-analytic case.