The Arctic is one of the most extreme terrestrial environments on the planet. Here, we present the first chromosome-scale genome assembly of a plant adapted to the high Arctic, Draba nivalis (Brassicaceae), an attractive model species for studying plant adaptation to the stresses imposed by this harsh environment. We used an iterative scaffolding strategy with data from short-reads, single-molecule long reads, proximity ligation data, and a genetic map to produce a 302 Mb assembly that is highly contiguous with 91.6% assembled into eight chromosomes (the base chromosome number). To identify candidate genes and gene families that may have facilitated adaptation to Arctic environmental stresses, we performed comparative genomic analyses with nine non-Arctic Brassicaceae species. We show that the D. nivalis genome contains expanded suites of genes associated with drought and cold stress (e.g., related to the maintenance of oxidation-reduction homeostasis, meiosis, and signaling pathways). The expansions of gene families associated with these functions appear to be driven in part by the activity of transposable elements. Tests of positive selection identify suites of candidate genes associated with meiosis and photoperiodism, as well as cold, drought, and oxidative stress responses. Our results reveal a multifaceted landscape of stress adaptation in the D. nivalis genome, offering avenues for the continued development of this species as an Arctic model plant.