  The search for Majorana bound states in solid-state physics has been limited
to materials which display a gap in their bulk spectrum. We show that such
unpaired states appear in certain quasi-one-dimensional Josephson junctions
arrays with gapless bulk excitations. The bulk modes mediate a coupling between
Majorana bound states via the Ruderman-Kittel-Yosida-Kasuya mechanism. As a
consequence, the lowest energy doublet acquires a finite energy difference. For
realistic set of parameters this energy splitting remains much smaller than the
energy of the bulk eigenstates even for short chains of length $L \sim 10$.
