Adsorption of methanethiol molecules from gas phase onto a Au(111) substrate is investigated by means of a molecular dynamics (MD) computer simulation. The problem that some of the elementary processes during adsorption take place on a time scale far too long to be handled by standard MD techniques is solved by making use of so-called "constrained or targeted dynamics". It is found that the lifetime against desorption out of the chemisorbed precursor state depends strongly on the coverage. It varies from 38 to 0.6 mu s between low and high coverage. The sticking coefficient is found to drop from >2 x 10(-3) to below 1 x 10(-5). By comparison with experimental data it is possible to determine a rate constant k similar to 65 s(-1) for the transition from the precursor state into the reactively adsorbed thiolate state.