Pure polyacetylene is a semiconductor, at best (band gap of about 2 eV). Peierls' theorem states that a one-dimensional metallic system is unstable with respect to a structural distortion to a lower energy state in which a band gap opens up at the Fermi level.
Doping of polyacetylenes, however, results in a substantial increase in conductivity - you need to either add or remove electrons, to form non-neutral solitons that can effectively migrate down the chain.