  We observe a giant spin-orbit splitting in bulk and surface states of the
non-centrosymmetric semiconductor BiTeI. We show that the Fermi level can be
placed in the valence or in the conduction band by controlling the surface
termination. In both cases it intersects spin-polarized bands, in the
corresponding surface depletion and accumulation layers. The momentum splitting
of these bands is not affected by adsorbate-induced changes in the surface
potential. These findings demonstrate that two properties crucial for enabling
semiconductor-based spin electronics -- a large, robust spin splitting and
ambipolar conduction -- are present in this material.
