  We discover a pair of spin-polarized surface bands on the (111) face of grey
arsenic by using angle-resolved photoemission spectroscopy (ARPES). In the
occupied side, the pair resembles typical nearly-free-electron Shockley states
observed on noble-metal surfaces. However, pump-probe ARPES reveals that the
spin-polarized pair traverses the bulk band gap and that the crossing of the
pair at $\bar\Gamma$ is topologically unavoidable. First-principles
calculations well reproduce the bands and their non-trivial topology; the
calculations also support that the surface states are of Shockley type because
they arise from a band inversion caused by crystal field. The results provide
compelling evidence that topological Shockley states are realized on As(111).
