  We study the possible stationary persistent supercurrents flowing on a
cylindrical sample supporting a two-dimensional charged fluid. The internal
dynamics of the fluid is obtained by means of an effective theory in which the
fluid self-interacts through a $U(1)$ gauge field. We find that the presence of
persistent supercurrents depends on what kind of gauge field it is. In
particular the current is zero if it is a Maxwell gauge field, and it is
maximal if it is a Chern-Simons gauge field. There is an intermediate behaviour
in presence of both Maxwell and Chern-Simons term. Therefore it appears that
persistent supercurrents are possible only if the fluid is chiral.
