Lens epithelium-derived growth factor (LEDGF/p75) tethers lentiviral preintegration complexes (PICs) to chromatin and is essential for effective HIV-1 replication. LEDGF/p75 interactions with lentiviral integrases are well characterized, but the structural basis for how LEDGF/p75 engages chromatin is unknown. We demonstrate that cellular LEDGF/p75 is tightly bound to mononucleosomes (MNs). Our proteomic experiments indicate that this interaction is direct and not mediated by other cellular factors. We determined the solution structure of LEDGF PWWP and monitored binding to the histone H3 tail containing trimethylated Lys36 (H3K36me3) and DNA by NMR. Results reveal two distinct functional interfaces of LEDGF PWWP: a well-defined hydrophobic cavity, which selectively interacts with the H3K36me3 peptide and adjacent basic surface, which non-specifically binds DNA. LEDGF PWWP exhibits nanomolar binding affinity to purified native MNs, but displays markedly lower affinities for the isolated H3K36me3 peptide and DNA. Furthermore, we show that LEDGF PWWP preferentially and tightly binds to in vitro reconstituted MNs containing a tri-methyl-lysine analogue at position 36 of H3 and not to their unmodified counterparts. We conclude that cooperative binding of the hydrophobic cavity and basic surface to the cognate histone peptide and DNA wrapped in MNs is essential for high-affinity binding to chromatin.