(TaSe4)2I is a one-dimensional conductor exhibiting a charge-density-wave transition at 263 K which is accompanied by non-linear effects of the electrical conductivity. The electrical anisotropy was confirmed previously by optical measurements which had shown a pronounced plasma edge for light polarized parallel to the metallic chains and a nearly constant reflectivity for the polarization direction perpendicular to the chain axis. The present extended optical investigations reveal a Peierls gap existing even at room temperature. The temperature dependence of this gap in the temperature range between 140 K and 420 K is reported and the consequences for the electrical transport properties are discussed.