Tightly controlled DNA replication and RNA transcription are essential for differentiation and tissue growth in multicellular organisms. Histone chaperones, including the FACT (facilitates chromatin transcription) complex, are central for these processes and act by mediating DNA access through nucleosome reorganisation. However, their roles in vertebrate organogenesis are poorly understood. Here, we report the identification of zebrafish mutants for the gene encoding Structure specific recognition protein 1a (Ssrp1a), which, together with Spt16, forms the FACT heterodimer. Focussing on the liver and eye, we show that zygotic Ssrp1a is essential for proliferation and differentiation during organogenesis. Specifically, gene expression indicative of progressive organ differentiation is disrupted and RNA transcription is globally reduced. Ssrp1a-deficient embryos exhibit DNA synthesis defects and prolonged S phase, uncovering a role distinct from that of Spt16, which promotes G1 phase progression. Gene deletion/replacement experiments in Drosophila show that Ssrp1b, Ssrp1a and N-terminal Ssrp1a, equivalent to the yeast homologue Pob3, can substitute Drosophila Ssrp function. These data suggest that (1) Ssrp1b does not compensate for Ssrp1a loss in the zebrafish embryo, probably owing to insufficient expression levels, and (2) despite fundamental structural differences, the mechanisms mediating DNA accessibility by FACT are conserved between yeast and metazoans. We propose that the essential functions of Ssrp1a in DNA replication and gene transcription, together with its dynamic spatiotemporal expression, ensure organ-specific differentiation and proportional growth, which are crucial for the forming embryo.