Although a defect in the DNA polymerase POLQ leads to ionizing radiation sensitivity in mammalian cells, the relevant enzymatic pathway has not been identified. Here we define the specific mechanism by which POLQ restricts harmful DNA instability. Our experiments show that Polq-null murine cells are selectively hypersensitive to DNA strand breaking agents, and that damage resistance requires the DNA polymerase activity of POLQ. Using a DNA break end joining assay in cells, we monitored repair of DNA ends with long 3′ single-stranded overhangs. End joining events retaining much of the overhang were dependent on POLQ, and independent of Ku70. To analyze the repair function in more detail, we examined immunoglobulin class switch joining between DNA segments in antibody genes. POLQ participates in end joining of a DNA break during immunoglobulin class-switching, producing insertions of base pairs at the joins with homology to IgH switch-region sequences. Biochemical experiments with purified human POLQ protein revealed the mechanism generating the insertions during DNA end joining, relying on the unique ability of POLQ to extend DNA from minimally paired primers. DNA breaks at the IgH locus can sometimes join with breaks in Myc, creating a chromosome translocation. We found a marked increase in Myc/IgH translocations in Polq-defective mice, showing that POLQ suppresses genomic instability and genome rearrangements originating at DNA double-strand breaks. This work clearly defines a role and mechanism for mammalian POLQ in an alternative end joining pathway that suppresses the formation of chromosomal translocations. Our findings depart from the prevailing view that alternative end joining processes are generically translocation-prone.