Nap1 is a histone chaperone involved in the nuclear import of H2A-H2B and nucleosome assembly. Here, we report the crystal structure of Nap1 bound to H2A-H2B together with in vitro and in vivo functional studies that elucidate the principles underlying Nap1-mediated H2A-H2B chaperoning and nucleosome assembly. A Nap1 dimer provides an acidic binding surface and asymmetrically engages a single H2A-H2B heterodimer. Oligomerization of the Nap1-H2A-H2B complex results in burial of surfaces required for deposition of H2A-H2B into nucleosomes. Chromatin immunoprecipitation-exonuclease (ChIP-exo) analysis shows that Nap1 is required for H2A-H2B deposition across the genome. Mutants that interfere with Nap1 oligomerization exhibit severe nucleosome assembly defects showing that oligomerization is essential for the chaperone function. These findings establish the molecular basis for Nap1-mediated H2A-H2B deposition and nucleosome assembly.