  We show that the three-junction SQUID device designed for the Josephson flux
qubit can be used to study quantum chaos when operated at high energies. In the
parameter region where the system is classically chaotic we analyze the
spectral statistics. The nearest neighbor distributions $P(s)$ are well fitted
by the Berry Robnik theory employing as free parameters the pure classical
measures of the chaotic and regular regions of phase space in the different
energy regions. The phase space representation of the wave functions is
obtained via the Husimi distributions and the localization of the states on
classical structures is analyzed.
