  We propose a Josephson junction array which can be tuned into an
unconventional insulating state by varying external magnetic field. This
insulating state retains a gap to half vortices; as a consequence, such array
with non-trivial global geometry exhibits a ground state degeneracy. This
degeneracy is protected from the effects of external noise. We compute the gaps
separating higher energy states from the degenerate ground state and we discuss
experiments probing the unusual properties of this insulator.
