Li4PS4I was recently discovered as a novel crystalline lithium ion conductor by applying a soft chemistry approach. It adopts a tetragonal structure type suggesting a three-dimensional migration pathway favorable for a high conductivity [S.J. Sedlmaier, Chem. Mater. 29 (2017) 1830]. Especially in view of the highly connected pathways for Li motion within a simple anion sublattice formed by PS43- and iodine anions, the conductivity measured from both impedance spectroscopy and NMR data appears to be rather small, and a negative influence of impurities and of grain boundaries effects was assumed. In order to shed light on the full potential of this material, we performed a theoretical study of Li4PS4I in the framework of density functional theory. After creating a structural model that accurately accounts for the partial occupancies determined by diffraction experiments, we performed molecular dynamics simulations, unraveled the diffusion mechanisms and calculated diffusion coefficients and the activation barrier for diffusion. The results of the theoretical study on both a crystalline and a glassy supercell imply that Li4PS4I is in fact a superionic conductor with a much higher conductivity than reported so far.