RAP80 plays a key role in signal transduction in the DNA damage response by recruiting proteins to DNA damage foci by binding K63-polyubiquitin chains with two tandem ubiquitin-interacting motifs (tUIM). It is generally recognized that the typically weak interaction between ubiquitin (Ub) and various recognition motifs is intensified by themes such as tandem recognition motifs and Ub polymerization to achieve biological relevance. However, it remains an intricate problem to develop a detailed molecular mechanism to describe the process that leads to amplification of the Ub signal. A battery of solution-state NMR methods and molecular dynamics simulations were used to demonstrate that RAP80-tUIM employs mono- and multivalent interactions with polyUb chains to achieve enhanced affinity in comparison to monoUb interactions for signal amplification. The enhanced affinity is balanced by unfavorable entropic effects that include partial quenching of rapid reorientation between individual UIM domains and individual Ub domains in the bound state. For the RAP80-tUIM-polyUb interaction, increases in affinity with increasing chain length are a result of increased numbers of mono- and multivalent binding sites in the longer polyUb chains. The mono- and multivalent interactions are characterized by intrinsically weak binding and fast off-rates; these weak interactions with fast kinetics may be an important factor underlying the transient nature of protein-protein interactions that comprise DNA damage foci.