Targeted sequencing enables sensitive and cost-effective analysis by focusing resources on molecules of interest. Existing methods, however, are limited in enrichment power and target capture length. Here, we present a novel method that uses compound nucleic acid cytometry to achieve million-fold enrichments of molecules >10 kbp in length using minimal prior target information. We demonstrate the approach by sequencing HIV proviruses in infected individuals. Our method is useful for rare target sequencing in research and clinical applications, including for identifying cancer-associated mutations or sequencing viruses infecting cells.