Chiral edge states are the hallmark of two- and three-dimensional topological materials,
but their one-dimensional (1D) analog has not yet been found. We report that the 1D
topological edge states, solitons, of the charge density wave system of indium atomic
wires self-assembled on a silicon surface have chirality. The system is described by a
coupled double Peierls-dimerized atomic chain, where the interchain coupling induces
dynamical sublattice symmetry breaking. This changes its topological symmetry from
Z2 Z2 to Z4 and endows solitons with a chiral degree of freedom. Chiral solitons can
produce quantized charge transport across the chain that is topologically protected and
controllable by the soliton’s chirality. Individual right- and left-chiral solitons in indium
wires are directly identified by scanning tunneling microscopy.