The view of plant-cell cytokinesis commonly depicted in textbooks is of a symmetrical process, with the phragmoplast initiating in the center of the cell and growing outward to the parental cell membrane. In contrast to this picture, we observe that cell-plate development in Arabidopsis shoot cells is highly polarized along the plane of division. Three-dimensional live-cell imaging reveals that the mitotic spindle and phragmoplast are laterally displaced, and that the growing cell plate anchors on one side of the cell at an early stage of cytokinesis. Growth of phragmoplast across the cell creates a new partition in its wake, giving the visual effect of a curtain being pulled across the cell. Throughout this process, the advancing front of the phragmoplast is in intimate contact with the parental wall, suggesting that short-range interactions between the phragmoplast and plasma membrane may play important roles in guiding the cell plate throughout much of its development. Polarized cytokinesis was observed in a wide variety of vacuolate shoot cells and in some small root cells, implying that it is not solely a function of cell size. This mode of cytokinesis may provide a mechanically robust mechanism for cell-plate formation in large cells and suggests a simple explanation for the occurrence of cell wall stubs observed upon drug treatment or in cytokinetic mutants.