Bacterial adaptive immunity and genome engineering involving the CRISPR (clustered regularly interspaced short palindromic repeats)-associated (Cas) protein Cas9 begin with RNA-guided DNA unwinding to form an RNA-DNA hybrid and a displaced DNA strand inside the protein. The role of this R-loop structure in positioning each DNA strand for cleavage by the two Cas9 nuclease domains is unknown. We determine molecular structures of the catalytically active Streptococcus pyogenes Cas9 R-loop that show the displaced DNA strand located near the RuvC nuclease domain active site. These protein-DNA interactions, in turn, position the HNH nuclease domain adjacent to the target DNA strand cleavage site in a conformation essential for concerted DNA cutting. Cas9 bends the DNA helix by 30 degrees, providing the structural distortion needed for R-loop formation.