A recent experimental observation has shown that torsional oscillations of engine camshafts induced by valve train loads can cause significant tension fluctuation in the timing chain and magnifies the chain transverse vibrations. This will result in an increase of the undesirable impact noise from the chain/sprocket meshing process, and the knocking noise from the interaction between the vibrating chain and the guides. Although many studies have been done on chain drives, the analysis to-date are not able to address these phenomena due to the assumptions made in the modelling process. This paper presents a generic model of an engine timing chain drive system which couples the sprocket motion with the vibrations of the chain spans. The effects of the cam torsional loads upon the total system are investigated based on this model. It is shown that the cam shaft oscillations will cause longitudinal vibrations in the chains and induce significant tension changes. This periodic tension variation could destablize the system and cause large transverse vibration of the chain spans. Parametric resonances are identified and the instability zones are derived through perturbation analysis using the Multiple Scale method. It is concluded that both the subharmonic type and the summation type parametric resonance exist. The contributions of various system parameters to the chain response and stability are quantified. Since the chain transverse vibration is a critical factor in determining the noise characteristic of chain drives, this analysis is an important step toward designing a quiet timing chain system.