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 0.25σ, 0.333σ, 0.40σ, 0.60σ and 0.80σ, where σ is the Lennard-Jones length scaling parameter. The results were used to determine the shear viscosity of n-alkanes in the zero-density limit by representing an n-alkane molecule as a rigid linear chain consisting of nc − 1 spherical segments, where nc 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.