  We study a one-dimensional Josephson junction chain embedded in a magnetic
field. We show that when the magnetic flux per elementary loop equals half the
superconducting flux quantum $\phi_0=h/2e$, a local $\nbZ_2$ symmetry arises.
This symmetry is responsible for a nematic Luttinger liquid state associated to
bound states of Cooper pairs. We analyze the phase diagram and we discuss some
experimental possibilities to observe this exotic phase.
