The blue shark Prionace glauca is the most abundant large pelagic shark in the Atlantic Ocean. Although recaptures of tagged sharks have shown that the species is highly migratory, migration pathways towards the overwintering grounds remain poorly understood. We used archival satellite pop-up tags to track 23 blue sharks over a mean period of 88 days as they departed the coastal waters of North America in the autumn. Within 1-2 days of entering the Gulf Stream (median date of 21 Oct), all sharks initiated a striking diel vertical migration, taking them from a mean nighttime depth of 74 m to a mean depth of 412 m during the day as they appeared to pursue vertically migrating squid and fish prey. Although functionally blind at depth, calculations suggest that there would be a ~2.5-fold thermoregulatory advantage to swimming and feeding in the markedly cooler deep waters, even if there was any reduced foraging success associated with the extreme depth. Noting that the Gulf Stream current speeds are reduced at depth, we used a detailed circulation model of the North Atlantic to examine the influence of the diving behaviour on the advection experienced by the sharks. However, there was no indication that the shark diving resulted in a significant modification of their net migratory pathway. The relative abundance of deep-diving sharks, swordfish, and sperm whales in the Gulf Stream and adjacent waters suggests that it may serve as a key winter feeding ground for large pelagic predators in the North Atlantic.