Shiny black, air-insensitive crystals of tellurium-rich one-dimensional coordination polymers were synthesized by melting a mixture of the elements with TeCl4. The compounds [Ru(Te9)](InCl4)2 and [Ru(Te8)]Cl2 crystallize in the monoclinic space group type C2/c, whereas [Rh(Te6)]Cl3 adopts the trigonal space group type Rc. In the crystal structures, linear, positively charged [Mm+(Ten±0)] (M=Ru, m=2; Rh, m=3) chains run parallel to the c axes. Each of the uncharged Ten molecules (n=6, 8, 9) coordinates two transition-metal atoms as a bridging bis-tridentate ligand. Because the coordinating tellurium atoms act as electron-pair donors, the 18-electron rule is fulfilled for the octahedrally coordinated transition-metal cations. Based on DFT calculations, the quantum theory of atoms in molecules (QTAIM) and the electron localizability indicator (ELI) provide insight into the principles of the polar donor bonding in these complexes. Comparison with optimized ring geometries reveals substantial tension in the coordinating tellurium molecules.