Most plane-polarized tissues are formed by identically oriented cells [1, 2]. A notable exception occurs in the vertebrate vestibular system and lateral-line neuromasts, where mechanosensory hair cells orient along a single axis but in opposite directions to generate bipolar epithelia [3-5]. In zebrafish neuromasts, pairs of hair cells arise from the division of a non-sensory progenitor [6, 7] and acquire opposing planar polarity via the asymmetric expression of the polarity-determinant transcription factor Emx2 [8-11]. Here, we reveal the initial symmetry-breaking step by decrypting the developmental trajectory of hair cells using single-cell RNA sequencing (scRNA-seq), diffusion pseudotime analysis, lineage tracing, and mutagenesis. We show that Emx2 is absent in non-sensory epithelial cells, begins expression in hair-cell progenitors, and is downregulated in one of the sibling hair cells via signaling through the Notch1a receptor. Analysis of Emx2-deficient specimens, in which every hair cell adopts an identical direction, indicates that Emx2 asymmetry does not result from auto-regulatory feedback. These data reveal a two-tiered mechanism by which the symmetric monodirectional ground state of the epithelium is inverted by deterministic initiation of Emx2 expression in hair-cell progenitors and a subsequent stochastic repression of Emx2 in one of the sibling hair cells breaks directional symmetry to establish planar bipolarity.