Cell division is a fundamental process of life, producing two cells from one single cell at each cell division. During animal development, a fertilized egg divides many times, increasing the number of cells, which are precisely organized within the animal’s body. How many times a cell undergoes cell division and how the two daughter cells are positioned after the division can be critical for shaping the animal. Although the machinery essential for cell division is well characterized and evolutionarily conserved, it remains unknown in most animals how a cell division can become oriented relative to the animal’s body axis. The work by Negishi et al., published recently in the electronic journal eLife, has revealed that in the sea squirt (Ciona intestinalis) embryo, the orientation of the cell division machinery in epithelial cells is controlled by a unique cell membrane structure, which we call an “invagination”.