Spin-polarized band structure of the three-dimensional quantum spin Hall insulator $\rm Bi_{1-x}Sb_{x}$ (x=0.12-0.13) was fully elucidated by spin-polarized angle-resolved photoemission spectroscopy using a high-yield spin polarimeter equipped with a high-resolution electron spectrometer. Between the two time-reversal-invariant points, $\bar{\varGamma}$ and $\bar{M}$, of the (111) surface Brillouin zone, a spin-up band ($\Sigma_3$ band) was found to cross the Fermi energy only once, providing unambiguous evidence for the strong topological insulator phase. The observed spin-polarized band dispersions determine the "mirror chirality" to be -1, which agrees with the theoretical prediction based on first-principles calculations.
