Cas3 nuclease-helicase is part of CRISPR immunity systems in many bacteria and archaea. In type I CRISPR, Cas3 nuclease degrades invader DNA that has been base-paired to crRNA as an R-loop within a “Cascade” complex. An R-loop is a DNA-RNA hybrid that includes a displaced single-strand DNA loop. Purified Cas3 from E. coliand the archaeon M. thermautrophicuscan process R-loops without DNA/RNA sequence specificity and without Cascade. This has potential to affect other aspects of microbial biology that involve R-loops. Regulatory RNAs and host cell proteins modulate replication of ColE1 plasmids (e.g., pUC) from R-loop primers. We observed that Cas3 could override endogenous control of a ColE1 replicon, stimulating uncontrolled (“runaway”) replication and resulting in much higher plasmid yields. This effect was absent when using helicase-defective Cas3 (Cas3K320L) or a non-ColE1 plasmid, and was dependent on RNaseHI. Cas3 also promoted formation of plasmid multimers or concatemers, a phenotype consistent with deregulated ColE1 replication and typical of cells lacking RNaseHI. These effects of Cas3 on ColE1 plasmids are inconsistent with it unwinding R-loops in vivo, at least in this assay. We discuss a model of how Cas3 might be able to regulate RNA molecules in vivo, unless it is targeted to CRISPR defense by Cascade, or kept in check by RecG and RNaseHI.