Visceral leishmaniasis is a potentially fatal disease endemic to large parts of Asia and Africa, primarily caused by the protozoan parasite Leishmania donovani. Here, we report a high-quality reference genome sequence for a strain of L. donovani from Nepal, and use this sequence to study variation in a set of 16 related clinical lines, isolated from visceral leishmaniasis patients from the same region, which also differ in their response to in vitro drug susceptibility. We show that whole-genome sequence data reveals genetic structure within these lines not shown by multilocus typing, and suggests that drug resistance has emerged multiple times in this closely related set of lines. Sequence comparisons with other Leishmania species and analysis of single-nucleotide diversity within our sample showed evidence of selection acting in a range of surface- and transport-related genes, including genes associated with drug resistance. Against a background of relative genetic homogeneity, we found extensive variation in chromosome copy number between our lines. Other forms of structural variation were significantly associated with drug resistance, notably including gene dosage and the copy number of an experimentally verified circular episome present in all lines and described here for the first time. This study provides a basis for more powerful molecular profiling of visceral leishmaniasis, providing additional power to track the drug resistance and epidemiology of an important human pathogen.