Most animal embryos display a delay in the activation of zygotic transcription during early embryogenesis [1]. This process is thought to help coordinate rapid increases in cell number during early development [2]. The timing of zygotic genome activation (ZGA) during the maternal-to-zygotic transition (MZT) remains uncertain despite extensive efforts. We explore ZGA in the simple protovertebrate, Ciona intestinalis. Single-cell RNA sequencing (RNA-seq) assays identified Cyclin B3 (Ccnb3) as a putative mediator of ZGA. Maternal Ccnb3 transcripts rapidly diminish in abundance during the onset of zygotic transcription at the 8-cell and 16-cell stages. Disruption of Ccnb3 activity results in precocious activation of zygotic transcription, while overexpression abolishes normal activation. These observations suggest that the depletion of maternal Cyclin B3 products is a critical component of the MZT and ZGA. We discuss evidence that this mechanism might play a conserved role in the MZT of other metazoans, including mice and humans.