Centrosome duplication is a critical step in assembly of the bipolar mitotic spindle, but the molecular mechanisms regulating this process during the cell cycle and during animal development are poorly understood. Here, we report that the zyg-1 gene of Caenorhabditis elegans is an essential regulator of centrosome duplication. ZYG-1 is a protein kinase specifically required for daughter centriole formation that localizes transiently to centrosomes and acts at least one cell cycle prior to each spindle assembly event. In the embryo, ZYG-1 participates in a unique regulatory scheme whereby paternal ZYG-1 regulates duplication and bipolar spindle assembly during the first cell cycle, and maternal ZYG-1 regulates these processes thereafter. ZYG-1 is therefore a key molecular component of the centrosome/centriole duplication process.