The layered polar semiconductor BiTeI exhibits large Rashba-type spin-orbit splittings in its bulk and surface electronic structure. Here we report an artificial structural modification near the surface of BiTeI(0001) induced by annealing in vacuum. Using scanning tunneling microscopy we show that the annealing-induced change in the near-surface stoichiometry results in a structural change from a non-centrosymmetric triple-layered to a quintuple-layered structure. The structural change gives rise to the emergence of topological surface states with helical spin texture as demonstrated by angle-resolved photoemission experiments and relativistic first-principles calculations. The results provide a way to modify the electronic structure of layered materials by a controlled manipulation of the atomic stacking sequences.