  I study the edge states of the topological exciton condensate formed by
Coulomb interaction between two parallel surfaces of a strong topological
insulator. When the condensate is contacted by superconductors with a {\pi}
phase shift across the two surfaces, a pair of counter-propagating Majorana
modes close the gap at the boundary. I propose a nano-structured system of
topological insulators and superconductors to realize unpaired Majorana
fermions. The Majorana signal can be used to detect the formation of the
topological exciton condensate. The relevant experimental signatures as well as
implications for related systems are discussed.
