HIV-1 integrase (IN) promotes encapsulation of viral genomic RNA into mature viral cores, and this function is a target for ongoing antiretroviral drug development efforts1-3. Here we determined the cryogenic electron microscopy (cryo-EM) structure of a primate lentiviral IN in a complex with RNA, revealing a linear filament made of IN octamer repeat units, each comprising a pair of asymmetric homotetramers. The assembly is stabilized through IN-RNA interactions involving mainly the IN C-terminal domains and RNA backbone. The spacing and orientation of the IN filament repeat units closely matched those of consecutive capsid (CA) hexamers within the mature CA lattice. Using cryo-EM images of native purified HIV-1 cores, we refined the structure of the IN filament as it propagates along the luminal side of the CA lattice. Each IN tetramer within the filament nestled in a CA hexamer, engaging closely with the major homology regions. Substitutions of residues involved in IN-CA contacts yielded eccentric virions with RNA nucleoids located outside of the cores. Collectively, our results establish the structural basis for the HIV-1 IN-RNA interaction and reveal that IN forms an RNA-binding module on the luminal side of the mature CA lattice.