The shear viscosity in the dilute gas limit has been calculated by means of the classical trajectory method for a gas consisting of chain-like molecules. The molecules were modelled as rigid chains made up of spherical segments that interact through a combination of site-site Lennard-Jones 12-6 potentials. Results are reported for chains consisting of 2, 3, 4, 6, 8, 12 and 16 segments in the reduced temperature range of 0.3 – 50 for site-site separations of 0.25 , 0.333 , 0.40 , 0.60 and 0.80 , where is the Lennard-Jones length scaling parameter. The results were used to determine the shear viscosity of n-alkanes in the zerodensity limit by representing an n-alkane molecule as a rigid linear chain consisting of c − 1 spherical segments, where c is the number of carbon atoms. We show that for a given n-alkane molecule, the scaling parameters ε and σ are not unique and not transferable from one molecule to another. The commonly used site-site Lennard-Jones 12-6 potential in combination with a rigid-chain molecular representation can only accurately mimic the viscosity if the scaling parameters are fitted. If the scaling parameters are estimated from the scaling parameters of other n-alkanes, the predicted viscosity values have an unacceptably high uncertainty