The chambered nautilus (Nautilus pompilius) encounters severe environmental hypoxia during diurnal vertical movements in the ocean. The metabolic cost of locomotion (Cmet) and swimming performance depend on how efficiently momentum is imparted to the water and how long on-board oxygen stores last. While propulsive efficiency is generally thought to be relatively low in jet propelled animals, the low Cmet in Nautilus indicates that this is not the case. We measured the wake structure in Nautilus during jet propulsion swimming, to determine their propulsive efficiency. Animals swam with either an anterior-first or posterior-first orientation. With increasing swimming speed, whole cycle propulsive efficiency increased during posterior-first swimming but decreased during anterior-first swimming, reaching a maximum of 0.76. The highest propulsive efficiencies were achieved by using an asymmetrical contractile cycle in which the fluid ejection phase was relatively longer than the refilling phase, reducing the volume flow rate of the ejected fluid. Our results demonstrate that a relatively high whole cycle propulsive efficiency underlies the low Cmet in Nautilus, representing a strategy to reduce the metabolic demands in an animal that spends a significant part of its daily life in a hypoxic environment.