Museum collections are essential for understanding biodiversity and next-generation sequencing methods (NGS) offer new opportunities to generate genomic data on specimens of extinct species for phylogenetic and other studies. Hesperelaea is a monotypic Oleaceae genus that was collected only once, 140 years ago on Guadalupe Island, Mexico. This lineage is almost certainly extinct, and has been considered an insular paleoendemic of unknown relationship within subtribe Oleinae. Here, a genome skimming approach was attempted on the H. palmeri specimen to generate genomic data in order to interpret the biogeographic history of Hesperelaea in a phylogenetic framework. Despite highly degraded DNA, we obtained the complete plastome, the nuclear ribosomal DNA cluster (nrDNA), and partial sequences of low-copy genes. Six plastid regions and nrDNA internal transcribed spacers were used for phylogenetic estimations of subtribe Oleinae, including data from previous studies. Bayesian and maximum likelihood phylogenies strongly place Hesperelaea within an American lineage that includes Forestiera and Priogymnanthus. Molecular dating suggests an Early Miocene divergence between Hesperelaea and its closest relatives. Our study thus confirms that Hesperelaea was a paleoendemic lineage that likely predates Guadalupe Island, and provides a notable example of the high potential of NGS for analyzing historical herbarium specimens and revolutionizing systematics.