In modern applications of molecular epidemiology, genetic sequence data are routinely used to identify clusters of transmission in rapidly evolving pathogens, most notably HIV-1. Traditional 'shoe-leather' epidemiology infers transmission clusters by tracing chains of partners sharing epidemiological connections (e.g., sexual contact). Here, we present a computational tool for identifying a molecular transmission analog of such clusters: HIV-TRACE (TRAnsmission Cluster Engine). HIV-TRACE implements an approach inspired by traditional epidemiology, by identifying chains of partners whose viral genetic relatedness imply direct or indirect epidemiological connections. Molecular transmission clusters are constructed using codon-aware pairwise alignment to a reference sequence followed by pairwise genetic distance estimation among all sequences. This approach is computationally tractable and is capable of identifying HIV-1 transmission clusters in large surveillance databases comprising tens or hundreds of thousands of sequences in near real time, that is, on the order of minutes to hours. HIV-TRACE is available at www.hivtrace.org and from www.github.com/veg/hivtrace, along with the accompanying result visualization module from www.github.com/veg/hivtrace-viz. Importantly, the approach underlying HIV-TRACE is not limited to the study of HIV-1 and can be applied to study outbreaks and epidemics of other rapidly evolving pathogens.