Not much is known about how organelles organize into patterns. In ciliates, the cortical pattern is propagated during “tandem duplication,” a cell division that remodels the parental cell into two daughter cells. A key step is the formation of the division boundary along the cell’s equator. In Tetrahymena thermophila, the cdaA alleles prevent the formation of the division boundary. We find that the CDAA gene encodes a cyclin E that accumulates in the posterior cell half, concurrently with accumulation of CdaI, a Hippo/Mst kinase, in the anterior cell half. The division boundary forms between the margins of expression of CdaI and CdaA, which exclude each other from their own cortical domains. The activities of CdaA and CdaI must be balanced to initiate the division boundary and to position it along the cell’s equator. CdaA and CdaI cooperate to position organelles near the new cell ends. Our data point to an intracellular positioning mechanism involving antagonistic Hippo signaling and cyclin E.