To understand how multiprotein complexes assemble and function on chromatin, we combined quantitative analysis of the mammalian nucleotide excision DNA repair (NER) machinery in living cells with computational modeling. We found that individual NER components exchange within tens of seconds between the bound state in repair complexes and the diffusive state in the nucleoplasm, whereas their net accumulation at repair sites evolves over several hours. Based on these in vivo data, we developed a predictive kinetic model for the assembly and function of repair complexes. DNA repair is orchestrated by the interplay of reversible protein-binding events and progressive enzymatic modifications of the chromatin substrate. We demonstrate that faithful recognition of DNA lesions is time consuming, whereas subsequently, repair complexes form rapidly through random and reversible assembly of NER proteins. Our kinetic analysis of the NER system reveals a fundamental conflict between specificity and efficiency of chromatin-associated protein machineries and shows how a trade off is negotiated through reversibility of protein binding.