We report the first two complete mitochondrial genome sequences of the thylacine (Thylacinus cynocephalus), or so-called Tasmanian tiger, extinct since 1936. The thylacine's phylogenetic position within australidelphian marsupials has long been debated, and here we provide strong support for the thylacine's basal position in Dasyuromorphia, aided by mitochondrial genome sequence that we generated from the extant numbat (Myrmecobius fasciatus). Surprisingly, both of our thylacine sequences differ by 11%-15% from putative thylacine mitochondrial genes in GenBank, with one of our samples originating from a direct offspring of the previously sequenced individual. Our data sample each mitochondrial nucleotide an average of 50 times, thereby providing the first high-fidelity reference sequence for thylacine population genetics. Our two sequences differ in only five nucleotides out of 15,452, hinting at a very low genetic diversity shortly before extinction. Despite the samples' heavy contamination with bacterial and human DNA and their temperate storage history, we estimate that as much as one-third of the total DNA in each sample is from the thylacine. The microbial content of the two thylacine samples was subjected to metagenomic analysis, and showed striking differences between a wild-captured individual and a born-in-captivity one. This study therefore adds to the growing evidence that extensive sequencing of museum collections is both feasible and desirable, and can yield complete genomes.