Separation of chiral molecules using achiral inputs is an interesting alternative to traditional techniques based on the chiral recognition mechanism. In this article we propose a lattice gas Monte Carlo model of two-dimensional chiral segregation induced by breaking of molecular orientational symmetry. Simulations were performed on a square lattice for rigid chain molecules composed of four and five identical segments. Mirror-image flat chain conformations resulting in different enantiomeric pairs were considered for each probe molecule. The enantiomers were assumed to interact via short-ranged segment-segment interaction potential limited to nearest neighbors on the lattice. We considered two qualitatively different situations in which (1) the molecules were allowed to rotate on the surface and adopt any of the four planar orientations and (2) the rotation was blocked, so that only one planar orientation was possible. The results obtained for the racemic overlayers showed clearly that the orientational symmetry breaking can induce spontaneous segregation of the enantiomers into large enantiopure domains. However, this effect was observed only for molecules with sufficiently long linear fragment. In the case of kinked bulky molecules a mixed assembly was formed, demonstrating the role of molecular shape in the orientationally biased segregation of enantiomers in adsorbed films. The insights from this study can be useful in developing strategies for 2D chiral separations in which external directional fields are used.