  Semiclassical theory predicts that the weak localization correction to the
conductance of a ballistic chaotic cavity is suppressed if the Ehrenfest time
exceeds the dwell time in the cavity [I. L. Aleiner and A. I. Larkin, Phys.
Rev. B {\bf 54}, 14424 (1996)]. We report numerical simulations of weak
localization in the open quantum kicked rotator that confirm this prediction.
Our results disagree with the `effective random matrix theory' of transport
through ballistic chaotic cavities.
