Retroviral integration is catalysed by a tetramer of integrase (IN) assembled on viral DNA ends in a stable complex, known as the intasome. How the intasome interfaces with chromosomal DNA, which exists in the form of nucleosomal arrays, is currently unknown. Here we show that the prototype foamy virus (PFV) intasome is proficient at stable capture of nucleosomes as targets for integration. Single-particle cryo-electron microscopy reveals a multivalent intasome–nucleosome interface involving both gyres of nucleosomal DNA and one H2A–H2B heterodimer. While the histone octamer remains intact, the DNA is lifted from the surface of the H2A–H2B heterodimer to allow integration at strongly preferred superhelix location ±3.5 positions. Amino acid substitutions disrupting these contacts impinge on the ability of the intasome to engage nucleosomes in vitro and redistribute viral integration sites on the genomic scale. Our findings elucidate the molecular basis for nucleosome capture by the viral DNA recombination machinery and the underlying nucleosome plasticity that allows integration.