It has been predicted, but never confirmed, that colloidal particles in a nematic liquid crystal could be self-assembled by delocalized topological defects and entangled disclinations. We show experimentally and theoretically that colloidal dimers and 1D structures bound by entangled topological defect loops can indeed be created by locally thermally quenching a thin layer of the nematic liquid crystal around selected colloidal particles. The topological entanglement provides a strong stringlike binding, which is ten thousand times stronger compared to water-based colloids. This unique binding mechanism could be used to assemble resonator optical waveguides and robust chiral and achiral structures of topologically entangled colloids that we call colloidal wires.