Changes in cell shape are a fundamental feature of animal development driving the formation of ordered tissues from disordered groups of cells. One common type of animal cell shape change is apical constriction, where a cell or group of cells shrinks down one side more than others. Here, we seek to understand the molecular underpinnings that drive apical constriction using a simplified model system, the roundworm Caenorhabditis elegans. Early in C. elegans development, the endoderm precursor (E) cells undergo apical constriction. This cell shape change drives the internalization of the E cells. Previous work showed that the molecular motor non-muscle myosin II (NMY-2 in C. elegans) is required for E cell internalization, and is enriched and activated at the apical side of E cells where it is thought to generate force by pulling on a meshwork of filamentous actin in the cell cortex. We use particle image velocimetry to show that NMY-2 tagged with green fluorescent protein (GFP) localizes into distinct punctae which undergo centripetally-directed flow in the apical cortex of the E cells. We show that this flow occurs, surprisingly, before the initiation of cell shape change. We use laser nanosurgery to show that tension is established in the E cells’ apical cortices prior to cell shape change, that this tension does not change as cells change shape, and that this tension exceeds that of a neighboring, non-apically constricting cell. This work suggests that apical constriction may be governed not by the activation of myosin dynamics, but by a molecular clutch mechanically linking apical myosin dynamics to cell-cell junctions. We, therefore, sought to characterize the molecular nature of cell-cell junctions in the E cells to identify components that may contribute to this molecular clutch. We started by tagging with GFP all three essential members of the C. elegans cadherin-catenin complex (CCC), a complex known to contribute (albeit, redundantly) to apical constriction in the E cells. Spinning disk confocal fluorescence microscopy revealed that HMP-1/α-catenin-GFP, GFP-HMP-2/β-catenin, and HMR-1/cadherin-GFP all enriched at apical junctions as the E cells were undergoing apical constriction. We next showed that some CCC components require others to enrich apically. For example, HMR-1/cadherin requires HMP-1/α-catenin to enrich apically, suggesting that linking to the contractile actomyosin cytoskeleton might be required for apical enrichment. To test this we disrupted myosin dynamics using a temperature sensitive allele of nmy-2 or by using RNA interference to disrupt mrck-1, a kinase required for myosin activation. Both treatments disrupted the apical localization of cadherin, indicating that myosin activity is required to establish an apicobasally polarized cell-cell junction in apically constricting cells.