Acoel embryos exhibit a unique form of development that some investigators argue is related to that found in polyclad turbellarians and coelomate spiralians, which display typical quartet spiral cleavage. We generated the first cell-lineage fate map for an acoel flatworm, Neochildia fusca, using modern intracellular lineage tracers to assess the degree of similarity between these distinct developmental programs. N. fusca develops via a “duet” cleavage pattern in which second cleavage occurs in a leiotropically oblique plane relative to the animal–vegetal axis. At the four-cell stage, the plane of first cleavage corresponds to the plane of bilateral symmetry. All remaining cleavages are symmetrical across the sagittal plane. No ectomesoderm is formed; the first three micromere duets generate only ectodermal derivatives. Endomesoderm, including the complex assemblage of circular, longitudinal, and oblique muscle fibers, as well as the peripheral and central parenchyma, is generated by both third duet macromeres. The cleavage pattern, fate map, and origins of mesoderm in N. fusca share little similarity to that exhibited by other spiralians, including the Platyhelminthes (e.g., polyclad turbellarians). These findings are considered in light of the possible evolutionary origins of the acoel duet cleavage program versus the more typical quartet spiral cleavage program. Finally, an understanding of the cell-lineage fate map allows us to interpret the results of earlier cell deletion studies examining the specification of cell fates within these embryos and reveals the existence of cell–cell inductive interactions in these embryos.