The protein deacetylase SIRT6 maintains cellular homeostasis through multiple pathways that include the deacetylation of histone H3 and repression of transcription. Prior work suggests that SIRT6 is associated with chromatin and can substantially reduce global levels of H3 acetylation, but how SIRT6 is able to accomplish this feat is unknown. Here, we describe an exquisitely tight interaction between SIRT6 and nucleosome core particles, in which a 2:1 enzyme:nucleosome complex assembles via asymmetric binding with distinct affinities. While both SIRT6 molecules associate with the acidic patch on the nucleosome, we find that the intrinsically disordered SIRT6 C-terminus promotes binding at the higher affinity site through recognition of nucleosomal DNA. Together, multivalent interactions couple productive binding to efficient deacetylation of histones on endogenous chromatin. Unique among histone deacetylases, SIRT6 possesses the intrinsic capacity to tightly interact with nucleosomes for efficient activity.