Some species responded successfully to prehistoric changes in climate [1, 2], while others failed to adapt and became extinct [3]. The factors that determine successful climate adaptation remain poorly understood. We constructed a reference genome and studied physiological adaptations in the Alpine marmot (Marmota marmota), a large ground-dwelling squirrel exquisitely adapted to the "ice-age" climate of the Pleistocene steppe [4, 5]. Since the disappearance of this habitat, the rodent persists in large numbers in the high-altitude Alpine meadow [6, 7]. Genome and metabolome showed evidence of adaptation consistent with cold climate, affecting white adipose tissue. Conversely, however, we found that the Alpine marmot has levels of genetic variation that are among the lowest for mammals, such that deleterious mutations are less effectively purged. Our data rule out typical explanations for low diversity, such as high levels of consanguineous mating, or a very recent bottleneck. Instead, ancient demographic reconstruction revealed that genetic diversity was lost during the climate shifts of the Pleistocene and has not recovered, despite the current high population size. We attribute this slow recovery to the marmot's adaptive life history. The case of the Alpine marmot reveals a complicated relationship between climatic changes, genetic diversity, and conservation status. It shows that species of extremely low genetic diversity can be very successful and persist over thousands of years, but also that climate-adapted life history can trap a species in a persistent state of low genetic diversity.