DNA in the eukaryotic nucleus is packaged in the form of nucleosomes, ~147 base pairs of DNA wrapped around a histone protein octamer. The position and histone composition of nucleosomes is governed by ATP dependent chromatin remodelers 1– 3 such as the 15 subunit INO80 complex 4. INO80 regulates gene expression, DNA repair and replication by sliding nucleosomes, exchanging histone H2A.Z with H2A, and positioning +1 and -1 nucleosomes at promoter DNA 5– 8. A structure and mechanism for these remodeling reactions is lacking. Here we report the cryo-electron microscopy structure at 4.3Å resolution, with parts at 3.7Å, of an evolutionary conserved core INO80 complex from Chaetomium thermophilum bound to a nucleosome. INO80 core cradles one entire gyre of the nucleosome through multivalent DNA and histone contacts. A Rvb1/2 AAA + ATPase hetero-hexamer is an assembly scaffold for the complex and acts as stator for the motor and nucleosome gripping subunits. The Swi2/Snf2 ATPase motor binds to SHL-6, unwraps ~15 base pairs, disrupts the H2A:DNA contacts and is poised to pump entry DNA into the nucleosome. Arp5-Ies6 grip SHL-2/-3 acting as counter grip for the motor on the other side of the H2A/H2B dimer. The Arp5 insertion domain forms a grappler element that binds the nucleosome dyad, connects the Arp5 core and entry DNA over a distance of ~90Å and packs against histone H2A/H2B near the acidic patch. Our structure together with biochemical data 8 suggest a unified mechanism for nucleosome sliding and histone editing by INO80. The motor pumps entry DNA across H2A/H2B against Arp5 and the grappler, sliding nucleosomes as a ratchet. Transient exposure of H2A/H2B by the motor and differential recognition of H2A.Z and H2A may regulate histone exchange during translocation.