We show that a metallic surface state is formed on Tl/Ge(111)-(1 × 1). The surface state forms electron pockets around K of the surface Brillouin zone. A first-principles calculation reveals that the electron pockets are composed of a single branch of a spin-split surface-state band. The spin quantization axis is along the surface normal and inverts according to the time-reversal symmetry. Since this spin-split branch is the unique metallic band on this surface, the surface conductivity should be governed by this spin-split branch, suggesting a possible spin-polarized electric current.