A Monte Carlo algorithm was developed and used to describe and explain previous experimental results associated with the kinetics of the uptake of chiral molecules on solid surfaces. The specific system simulated in this study is the adsorption of propylene oxide (PO) on Pt(111) surfaces. The surface was represented by a square lattice, and the time evolution of the adsorption, starting from a clean surface, was simulated via a number of sequential events chosen using a stochastic approach based on the so-called Master equation and derived from the formalism advanced by Gillespie. Two main assumptions were required to explain the experimental results: (1) that adsorption is assisted by previously adsorbed molecules, that is, that the probability for sticking is higher next to other adsorbates than on empty isolated sites, and (2) that the geometry adopted by the new adsorbate next to an old one is defined and different for homochiral versus heterochiral pairs. Our model was able to quantitatively reproduce the experimental data and to explain a number of important observations associated with the fact that the adsorbates are chiral, including the following: (1) the final PO saturation depends on the enantiocomposition of the gas phase, yielding a layer approximately 20% less dense with a racemic mixture than with enantiopure S-PO or R-PO; (2) the same changes in saturation coverages are seen if PO of different chirality are dosed sequentially; (3) the sticking probability is also higher with enantiopure adsorbates, at least in the initial stages of the uptake; (4) the sticking probability initially increases with increasing exposure, until reaching a maximum at about 20% of saturation; and (5) the adsorbed layers do not show any long-range ordering but display small linear clusters. It was also possible to reproduce the experimental observation that the addition of a prochiral molecule such as propylene (Py) to a surface dosed with a small amount of a chiral "seed" (PO) leads to an amplification of the initial enantioselectivity of that surface.