  Chiral order of the Josephson-junction ladder with half a flux quantum per
plaquette is studied by means of the exact diagonalization method. We consider
an extreme quantum limit where each superconductor grain (order parameter) is
represented by S=1/2 spin. So far, the semi-classical S -> \infty case, where
each spin reduces to a plane rotator, has been considered extensively. We found
that in the case of S=1/2, owing to the strong quantum fluctuations, the chiral
(vortex lattice) order becomes dissolved except in a region, where attractive
intrachain and, to our surprise, repulsive interchain interactions both exist.
On the contrary, for considerably wide range of parameters, the superconductor
(XY) order is kept critical. The present results are regarded as a
demonstration of the critical phase accompanying chiral-symmetry breaking
predicted for frustrated XXZ chain field-theoretically.
