Proper positioning of cells is essential for many aspects of development. Daughter cell positions can be specified via orienting the cell division axis during cytokinesis. Rotatory actomyosin flows during division have been implied in specifying and reorienting the cell division axis, but how general such reorientation events are, and how they are controlled, remains unclear. We followed the first nine divisions of Caenorhabditis elegans embryo development and demonstrate that chiral counter-rotating flows arise systematically in early AB lineage, but not in early P/EMS lineage cell divisions. Combining our experiments with thin film active chiral fluid theory we identify a mechanism by which chiral counter-rotating actomyosin flows arise in the AB lineage only, and show that they drive lineage-specific spindle skew and cell reorientation events. In conclusion, our work sheds light on the physical processes that underlie chiral morphogenesis in early development.