The basic helix-loop-helix PER-ARNT-SIM (bHLH-PAS) transcription factor CLOCK:BMAL1 interacts with E-box motifs in the context of nucleosomes to elicit a circadian pattern of gene expression that oscillates with approximately 24 hour periodicity. Core clock genes and other highly rhythmic targets of CLOCK:BMAL1 typically possess a tandem arrangement of E-boxes that is required for robust oscillations. Here, we show that the presence of tandem E-boxes enables CLOCK:BMAL1 to bind more internal sites on the nucleosome, leading to release of DNA from the histone core and the presentation of multiple coactivator binding motifs in close proximity to facilitate multivalent interactions with the coactivator CBP/p300. We show that the transactivation domain (TAD) of BMAL1, essential for CLOCK:BMAL1 activity, interacts with several modular domains of CBP. Deletion of these CBP domains or chemical inhibition of protein-protein interactions with CBP significantly reduces or eliminates CLOCK:BMAL1-driven activity. Altogether, this suggests that multivalent interactions with CBP may play a role in the ability of tandem CLOCK:BMAL1 heterodimers to recruit this limiting cofactor in cells.