  We study a model of two concentric onedimensional rings with incommensurate
areas $A_1$ and $A_2$, in a constant magnetic field. The two rings are coupled
by a nonhomogeneous inter-ring tunneling amplitude, which makes the
one-particle spectrum chaotic. For noninteracting particles the energy of the
many-body ground state and the first excited state exhibit random fluctuations
characterized by the Wigner-Dyson statistics. In contrast, we show that the
electron-electron interaction orders the magnetic field dependence of these
quantities, forcing them to become periodic functions, with period $ \propto
1/(A_1 + A_2)$. In such a strongly correlated system the only possible source
of disorder comes from charge fluctuations, which can be controlled by a
tunable inter-ring gate voltage.
