Cyclic guanosine monophosphate (GMP)–adenosine monophosphate (AMP) synthase (cGAS) recognizes cytosolic foreign or damaged DNA to activate the innate immune response to infection, inflammatory diseases, and cancer. By contrast, cGAS reactivity against self-DNA in the nucleus is suppressed by chromatin tethering. We report a 3.3-angstrom-resolution cryo–electron microscopy structure of cGAS in complex with the nucleosome core particle. The structure reveals that cGAS uses two conserved arginines to anchor to the nucleosome acidic patch. The nucleosome-binding interface exclusively occupies the strong double-stranded DNA (dsDNA)–binding surface on cGAS and sterically prevents cGAS from oligomerizing into the functionally active 2:2 cGAS-dsDNA state. These findings provide a structural basis for how cGAS maintains an inhibited state in the nucleus and further exemplify the role of the nucleosome in regulating diverse nuclear protein functions.