The search for one-dimensional (1D) topologically protected electronic states has become an important research goal for condensed matter physics owing to their potential use in spintronic devices or as a building block for topologically nontrivial electronic states. Using low temperature scanning tunneling microscopy, we demonstrate the formation of 1D electronic states at twin boundaries at the surface of the noncentrosymmetric material BiPd. These twin boundaries are topological defects that separate regions with antiparallel orientations of the crystallographic b axis. We demonstrate that the formation of the 1D electronic states can be rationalized by a change in effective mass of two-dimensional surface states across the twin boundary. Our work therefore reveals a novel route towards designing 1D electronic states with strong spin-orbit coupling.