The development of cell polarity is an essential prerequisite for tissue morphogenesis during embryogenesis, particularly in the development of epithelia. In addition, oriented cell division can have a powerful influence on tissue morphogenesis. Here we identify a novel mode of polarized cell division that generates pairs of neural progenitors with mirror-symmetric polarity in the developing zebrafish neural tube and has dramatic consequences for the organization of embryonic tissue. We show that during neural rod formation the polarity protein Pard3 is localized to the cleavage furrow of dividing progenitors, and then mirror-symmetrically inherited by the two daughter cells. This allows the daughter cells to integrate into opposite sides of the developing neural tube. Furthermore, these mirror-symmetric divisions have powerful morphogenetic influence: when forced to occur in ectopic locations during neurulation, they orchestrate the development of mirror-image pattern formation and the consequent generation of ectopic neural tubes.