Thousands of swarming honey bees (Apis mellifera) hang from a tree branch for hours while scout bees search for a new hive. This is a dangerous time in the life of a bee colony: the bees are exposed to weather and predators, and if the queen does not survive, neither will the colony. The bees form large clusters consisting entirely of bees hanging from each other, surrounding the queen. We investigate how bees arrange themselves within a swarm by probing swarms of 5,000 to 10,000 bees with x-ray computed tomography. The swarm hangs from a flat circular board to which the queen is attached, preventing the swarm from leaving. We find that the density of bees is highest closest to the attachment surface, where bees arrange themselves in layers for stability. The density of bees decreases towards the tip of the swarm. We track individual bees within the swarm to find evidence of division of labor between the bees. Most bees are arranged in nearly immobile structures, and the remainder of the bees are free to roam within the less dense areas of the swarm. Thus, a honey bee swarm self-organizes into a living structure that distributes loads among the bees, maintains structural stability, and responds to external stimuli.