CRISPR (clustered regularly interspaced short palindromic repeat)/Cas (CRISPR-associated) is a nucleic acid processing system in bacteria and archaea that interacts with mobile genetic elements. CRISPR DNA and RNA sequences are processed by Cas proteins: in Escherichia coli K-12, one CRISPR locus links to eight cas genes (cas1, 2, 3 and casABCDE), whose protein products promote protection against phage. In the present paper, we report that purified E. coli Cas3 catalyses ATP-independent annealing of RNA with DNA forming R-loops, hybrids of RNA base-paired into duplex DNA. ATP abolishes Cas3 R-loop formation and instead powers Cas3 helicase unwinding of the invading RNA strand of a model R-loop substrate. R-loop formation by Cas3 requires magnesium as a co-factor and is inactivated by mutagenesis of a conserved amino acid motif. Cells expressing the mutant Cas3 protein are more sensitive to plaque formation by the phage λvir. A complex of CasABCDE ('Cascade') also promotes R-loop formation and we discuss possible overlapping roles of Cas3 and Cascade in E. coli, and the apparently antagonistic roles of Cas3 catalysing RNA-DNA annealing and ATP-dependent helicase unwinding.