The first heterogeneous catalyst which affords polymerization of substituted acetylenes into readily available high molecular weight polymers is reported. The catalyst (Rh/PBI) has been prepared by supporting di-mu-chloro-bis(eta4-cycloocta-1,5-diene)dirhodium(I), [Rh(cod)Cl]2, on commercial polybenzimidazole (PBI) porous beads by means of a simple quantitative adsorption from THF solution, and tested in polymerization of phenylacetylene, 4-fluorophenylacetylene, and 4-pentylphenylacetylene. The polymer molecules formed were found to be released from the Rh/PBI to surrounding solution during the polymerization performed in THF. Formation of high molecular weight ((M)w values up to 325,000) polymers in prevailing cis-transoid configuration has been observed with all monomers. In a comparison with free [Rh(cod)Cl]2 used as the homogeneous catalyst, the Rh/PBI can be used repeatedly, exhibits somewhat lower polymerization activity but almost no oligomerization activity, and provides polymers of higher molecular weight.