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 ${$φ${}}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}h/2e$, a local ${Z}_{2}$ symmetry arises. This symmetry is responsible for a nematic Luttinger liquid state associated with bound states of Cooper pairs. We analyze the phase diagram and discuss some experimental possibilities to observe this exotic phase.