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Chromosomal rearrangements are essential events in the pathogenesis of both malignant and nonmalignant disorders, yet the factors affecting their formation are incompletely understood. Here we develop a zinc-finger nuclease translocation reporter and screen for factors that modulate rearrangements in human cells. We identify UBC9 and RAD50 as suppressors and 53BP1, DDB1 and poly(ADP)ribose polymerase 3 (PARP3) as promoters of chromosomal rearrangements across human cell types. We focus on PARP3 as it is dispensable for murine viability and has druggable catalytic activity. We find that PARP3 regulates G quadruplex (G4) DNA in response to DNA damage, which suppresses repair by nonhomologous end-joining and homologous recombination. Chemical stabilization of G4 DNA in PARP3 cells leads to widespread DNA double-strand breaks and synthetic lethality. We propose a model in which PARP3 suppresses G4 DNA and facilitates DNA repair by multiple pathways.