DNA replication is a major source of endogenous DNA damage in tumor cells and a key target of cellular response to genotoxic stress. DNA replication can be deregulated by oncoproteins, such as transcription factor MYC, aberrantly activated in many human cancers. MYC is stringently regulated by the ubiquitin system - for example, ubiquitination controls recruitment of the elongation factor PAF1c, instrumental in MYC activity. Curiously, a key MYC-targeting deubiquitinase USP28 also controls cellular response to DNA damage via the mediator protein 53BP1. USP28 forms stable dimers, but the biological role of USP28 dimerization is unknown. We show here that dimerization limits USP28 activity and restricts recruitment of PAF1c by MYC. Expression of monomeric USP28 stabilizes MYC and promotes PAF1c recruitment, leading to ectopic DNA synthesis and replication-associated DNA damage. USP28 dimerization is stimulated by 53BP1, which selectively binds USP28 dimers. Genotoxic stress diminishes 53BP1-USP28 interaction, promotes disassembly of USP28 dimers and stimulates PAF1c recruitment by MYC. This triggers firing of DNA replication origins during early response to genotoxins and exacerbates DNA damage. We propose that dimerization of USP28 prevents ectopic DNA replication at transcriptionally active chromatin to maintain genome stability.