Trypanosomes and Leishmania, protozoans that cause major human diseases, have a topologically intricate mitochondrial DNA (kinetoplast or kDNA) in the form of a network of thousands of interlocked circles. This unusual system provides a useful reporter for studying topoisomerase functions in vivo. We now find that these organisms have three type IA topoisomerases, one of which is phylogenetically distinctive and which we designate topoisomerase IA(mt). In Trypanosoma brucei topoisomerase IA(mt) immunolocalizes within the mitochondrion close to the kDNA disk in patterns that vary with the cell cycle. When expression of TOPIA(mt) is silenced by RNAi there is a striking accumulation of kDNA late theta structure replication intermediates, with subsequent loss of kDNA networks and halt in cell growth. This essential enzyme provides clear molecular evidence for the obligatory role of a type IA enzyme in the resolution of late theta structures in vivo. With no close orthologue in humans it also offers a target for the rational development of selectively toxic new antiprotozoal therapies.