We show with systematic photoemission spectroscopy and scanning tunneling spectroscopy data that a spin helical surface state appears on the (110) surface of noncentrosymmetric, three-dimensional HgTe. The topological surface state in HgTe exhibits sharp, linear dispersion without kz variation, as well as clear, left-right imbalanced spin polarization and circular dichroism. Chemical gating by alkali metal deposition on the surface causes the unexpected opening and/or increase of a surface insulating gap without changing its topological property. Such an unusual behavior we uncover in three-dimensional HgTe sheds light on a convenient control of the Fermi surface and quantum transport in a topological insulator.