This paper introduces the possibility of using the metastable persistent‐current quantum states of liquid helium II observed in superleaks as the principal element of an extremely stable gyroscope. It is suggested that combining the advantages of the nondecaying angular momentum inherent in the superleak with the suspension technique devised by Ensley could result in unprecedented stability and accuracy. An idealized system is described and two simple physical situations are analyzed. An interesting effect peculiar to this system is predicted. We find that temperature fluctuations, by transferring angular momentum in and out of the supercurrent state, drive the float containing the superleak into rotation. This rotation depends only on the nature of the fluctuations and the persistent current state. On the basis of the analysis of the simplified system described we conclude that a supercurrent gyroscope is quite feasible with existing technology.