A hallmark of histone H3 lysine 9 (H3K9)-methylated heterochromatin, conserved from the fission yeast Schizosaccharomyces pombe to humans, is its ability to spread to adjacent genomic regions(1-6). Central to heterochromatin spread is heterochromatin protein 1 (HP1), which recognizes H3K9-methylated chromatin, oligomerizes and forms a versatile platform that participates in diverse nuclear functions, ranging from gene silencing to chromosome segregation(1-6). How HP1 proteins assemble on methylated nucleosomal templates and how the HP1-nucleosome complex achieves functional versatility remain poorly understood. Here we show that binding of the key S. pombe HP1 protein, Swi6, to methylated nucleosomes drives a switch from an auto-inhibited state to a spreading-competent state. In the auto-inhibited state, a histonemimic sequence in one Swi6 monomer blocks methyl-mark recognition by the chromodomain of another monomer. Auto-inhibition is relieved by recognition of two template features, the H3K9 methyl mark and nucleosomal DNA. Cryo-electron-microscopy-based reconstruction of the Swi6-nucleosome complex provides the overall architecture of the spreading-competent state in which two unbound chromodomain sticky ends appear exposed. Disruption of the switch between the auto-inhibited and spreading-competent states disrupts heterochromatin assembly and gene silencing in vivo. These findings are reminiscent of other conditionally activated polymerization processes, such as actin nucleation, and open up a new class of regulatory mechanisms that operate on chromatin in vivo.