One-dimensional grain boundaries of two-dimensional semiconducting MX2 (M=Mo,W;X=S,Se) transition metal dichalcogenides are typically metallic at room temperature. The metallicity has its origin in the lattice polarization, which for these lattices with D3h symmetry is a topological invariant, and leads to one-dimensional boundary states inside the band gap. For boundaries perpendicular to the polarization direction, these states are necessarily 1/3 occupied by electrons or holes, making them susceptible to a metal-insulator transition that triples the translation period. Using density-functional-theory calculations, we demonstrate the emergence of combined one-dimensional spin density/charge density waves of that period at the boundary, opening up a small band gap of ∼0.1eV. This unique electronic structure allows for soliton excitations at the boundary that carry a fractional charge of ±1/3e.