Adaptive immunity in bacteria involves RNA-guided surveillance complexes that use CRISPR (clustered regularly interspaced short palindromic repeats)-associated (Cas) proteins together with CRISPR RNAs (crRNAs) to target invasive nucleic acids for degradation. Whereas type I and type II CRISPR-Cas surveillance complexes target double-stranded DNA, type III complexes target single-stranded RNA. Near-atomic resolution cryo-electron microscopy reconstructions of native type III Cmr (CRISPR RAMP module) complexes in the absence and presence of target RNA reveal a helical protein arrangement that positions the crRNA for substrate binding. Thumblike b hairpins intercalate between segments of duplexed crRNA: target RNA to facilitate cleavage of the target at 6-nucleotide intervals. The Cmr complex is architecturally similar to the type I CRISPR-Cascade complex, suggesting divergent evolution of these immune systems from a common ancestor.