Combinatorial polyvalent contacts of histone-binding domains or readers commonly mediate localization and activities of chromatin-associated proteins. A pair of readers, the PHD fingers of the protein CHD4, has been shown to bivalently recognize histone H3 tails. Here we describe a mechanism by which these linked but independent readers bind to the intact nucleosome core particle (NCP). Comprehensive NMR, chemical reactivity, molecular dynamics, and fluorescence analyses point to the critical roles of intra-nucleosomal histone-DNA interactions that reduce the accessibility of H3 tails in NCP, the nucleosomal DNA, and the linker between readers in modulating nucleosome- and/or histone-binding activities of the readers. We show that the second PHD finger of CHD4 initiates recruitment to the nucleosome, however both PHDs are required to alter the NCP dynamics. Our findings reveal a distinctive regulatory mechanism for the association of paired readers with the nucleosome that provides an intricate balance between cooperative and individual activities of the readers.