Pathogen-derived nucleic acids induce potent innate immune responses1-6. Cyclic GMP-AMP synthase (cGAS) is a dsDNA sensor that catalyzes the synthesis of a cyclic dinucleotide cGAMP, which mediates the induction of type I interferons through the STING-TBK1-IRF3 signaling axis7-11. It was widely accepted that cGAS is not reactive to self-DNA due to its cytosolic localization2,12,13. However, recent studies revealed that cGAS is mostly localized in the nucleus and tight nuclear tethering keeps cGAS inactive14-18. Here we show that cGAS binds to nucleosomes with nanomolar affinity and nucleosome binding potently inhibits the catalytic activity of cGAS. To elucidate the molecular basis of cGAS inactivation by nuclear tethering, we have determined the structure of mouse cGAS bound to human nucleosome by cryo-EM. The structure shows that cGAS binds to a negatively charged acidic patch formed by histone H2A and H2B via its second DNA binding site19. High affinity nucleosome binding blocks dsDNA binding and keeps cGAS in an inactive conformation. Mutations of cGAS that disrupt nucleosome binding dramatically affect cGAS mediated signaling in cells.