We have extended the chiral Gay-Berne (GB) pair potential of Memmer and co-workers [Liq. Cryst. (15), 345 (1993)] to the general case of biaxial ellipsoids, and we provide explicit expressions for the gradient and the torques to be used in molecular dynamics (MD) codes. To test our results against published results we have performed MD simulations of samples formed by N = 1024 uniaxial GB ellipsoids with constant volume, and we have studied how the thermotropic behavior is affected by particle chirality. We have run temperature scans starting from isotropic samples and found clear signatures of the spontaneous formation of both lower temperature blue and cholesteric phases.