We report the results of computer simulation studies for a bulk system composed of chiral particles interacting via the Gay-Berne potential and an additive chiral potential. Using Monte Carlo (MC) simulations in theNVTensemble, the chirality-temperature plane of the phase diagram was studied at different points by a variation of the chirality parametercdescribing the strength of the chiral potential. Additionally to the well-known isotropic, nematic and smectic phases of the Gay-Berne fluid, we localized regions of cholesteric phase. For large values of the chirality parameter we also observed blue phases. Furthermore, when starting from a cholesteric phase and decreasing the temperature at constantc, we obtained a phase region showing characteristics of the recently discovered helical smectic A* phase. All phases have been characterized by correlation functions, order parameters, and visual representations of selected configurations. All results of the simulation are limited by the small system size ofN= 256 molecules and the use of periodic boundary conditions.