  We study the nature of (001) surface states in Pb_{0.73}Sn_{0.27}Se in the
newly discovered topological-crystalline-insulator (TCI) phase as well as the
corresponding topologically trivial state above the band-gap-inversion
temperature. Our calculations predict not only metallic surface states with a
nontrivial chiral spin structure for the TCI case, but also nonmetallic
(gapped) surface states with nonzero spin polarization when the system is a
normal insulator. For both phases, angle- and spin-resolved photoelectron
spectroscopy measurements provide conclusive evidence for the formation of
these (001) surface states in Pb_{0.73}Sn_{0.27}Se, as well as for their chiral
spin structure.
