Methods are needed to study single molecules to reveal variability, interactions and mechanisms that may go undetected at the level of populations of molecules. We describe here an integrated series of reaction steps that allow individual nucleic acid molecules to be detected with excellent specificity. Oligonucleotide probes are circularized after hybridization to target sequences that have been prepared so that localized amplification reactions can be initiated from the target molecules. The process results in strong, discrete detection signals anchored to the target molecules. We use the method to observe the distribution, within and among human cells, of individual normal and mutant mitochondrial genomes that differ at a single nucleotide position.