Topological states are currently gathering intensive investigation in condensed matter physics due to their potential as configurable electronic devices for the future era coined “topotronics.” Beyond numerous breakthroughs in magnetism over the past decade, a new paradigm is emerging with the proposal of topologically protected objects in ferroelectric materials. Recently, ferroelectric skyrmions and vortices are observed in PbTiO₃/SrTiO₃ superlattices, opening the path toward ultra-small topological objects with low-power electric-field control. Here, the observation of chiral polar windings in a single epitaxial thin film, triggered by its self-organized stripe domain pattern arrangement, is reported. Combining resonant elastic X-ray scattering and scanning transmission electron microscopy, signatures of polar chirality in epitaxial BiFeO₃ thin films corroborated with a complex ferroelectric domain wall structure are shown. The net chirality suggests that domain walls induce a polar rotation through a small path alternating with an unexpected long path at every second domain wall. In addition, scanning probe microscopy reveals singularities associated to this peculiar domain wall structure. These results bring new insights into the unexpected complexity of standard striped-domain BiFeO₃ thin films and open questions as for the driving force of this polar chirality.