The helical twisting power beta(M) determines the pitch of the chiral nematic phase produced when a nematic liquid crystal is doped with a low concentration of chiral solute molecules. Molecules with large beta(M) values have potential applications in electro-optic displays and in optical data storage. This paper describes a new simulation technique which allows the prediction of both the sign and magnitude of beta(M). The method employs Monte Carlo simulations of a fully atomistic model of a chiral dopant in the presence of a twisted nematic solvent composed of Gay-Berne particles. Calculations are presented for five different chiral dopants, with results that are in good agreement with existing experimental data.