  Achieving true bulk insulating behavior in Bi$_2$Se$_3$, the archetypal
topological insulator with a simplistic one-band electronic structure and
sizable band gap, has been prohibited by a well-known self-doping effect caused
by selenium vacancies, whose extra electrons shift the chemical potential into
the bulk conduction band. We report a new synthesis method for achieving
stoichiometric Bi$_2$Se$_3$ crystals that exhibit nonmetallic behavior in
electrical transport down to low temperatures. Hall effect measurements
indicate the presence of both electron- and hole-like carriers, with the latter
identified with surface state conduction and the achievement of ambipolar
transport in bulk Bi$_2$Se$_3$ crystals without gating techniques. With carrier
mobilities surpassing the highest values yet reported for topological surface
states in this material, the achievement of ambipolar transport via upward band
bending is found to provide a key method to advancing the potential of this
material for future study and applications.
