A group contribution method is proposed for the estimation of second virial coefficients and dilute gas transport properties. In earlier work, the group contribution concept was applied to the Kihara potential function for teh calculation of second virial coefficients. In this study, the Chapman-Enskog theory is used to extend the method to viscosity and diffusivity for dilute gases. Applications are made to normal and branched alkanes, alkenes, nitrogen, and carbon dioxide, as well as to a variety of mixtures of these compounds. Group parameters beyond those presented earlier are provided. Parameters evaluated from second virial coefficient and viscosity data for pure hydrocarbons are found to predict accurate second virial cross coefficients, mixture viscosities and binary diffusivities for hydrocarbon mixtures. Group parameters evaluated from second virial cross coefficient data for mixtures of nitrogen or carbon dioxide with an alkane are found to provide good predictions of mixture viscosities and binary diffusivities for these systems.