  An odd number of gapless Dirac fermions is guaranteed to exist at a surface
of a strong topological insulator. We show that in a thin-film geometry and
under external bias, electron-hole pairs that reside in these surface states
can condense to form a coherent exciton condensate, similar in general terms to
the exciton condensate recently argued to exist in a biased graphene bilayer,
but with different topological properties. Such a `topological' exciton
condensate (TEC) exhibits a host of unusual properties; the most interesting
among them is the fractional charge +-e/2 carried by a singly quantized vortex
in the TEC order parameter.
