Asymmetric cell division (ACD) requires protein polarization in the mother cell to produce daughter cells with distinct identities (cell-fate asymmetry). Here, we define a previously undocumented mechanism for establishing cell-fate asymmetry in Arabidopsis stomatal stem cells. In particular, we show that polarization of the protein phosphatase BSL1 promotes stomatal ACD by establishing kinase-based signalling asymmetry in the two daughter cells. BSL1 polarization in the stomatal ACD mother cell is triggered at the onset of mitosis. Polarized BSL1 is inherited by the differentiating daughter cell, where it suppresses cell division and promotes cell-fate determination. Plants lacking BSL proteins exhibit stomatal overproliferation, which demonstrates that the BSL family plays an essential role in stomatal development. Our findings establish that BSL1 polarization provides a spatiotemporal molecular switch that enables cell-fate asymmetry in stomatal ACD daughter cells. We propose that BSL1 polarization is triggered by an ACD checkpoint in the mother cell that monitors the establishment of division-plane asymmetry.