Somites are segmental units of the mesoderm in vertebrate embryos that give rise to the axial skeleton, muscle, and dermis. Somitogenesis occurs in a periodic manner and is governed by a segmentation clock that causes cells to undergo repeated oscillations of gene expression. Here, we present a detailed analysis of cis-regulatory elements that control oscillating expression of the zebrafish her1 gene in the anterior presomitic mesoderm. We identify binding sites for Her proteins and demonstrate that they are necessary for transcriptional repression. This result confirms that direct negative autoregulation of her gene expression constitutes part of the oscillator mechanism. We also characterize binding sites for fused somites/Tbx24 and Suppressor of Hairless proteins and show that they are required for activation of her1 expression. These data provide the foundation for a precise description of the regulatory grammar that defines oscillating gene expression in the zebrafish segmentation clock.