Motivated by experimental studies of two-dimensional Ostwald ripening on Au(100) electrodes in chlorine-containing electrolytes, we have studied diffusion processes using density functional theory. We find that chlorine has a propensity to temporary form AuCl complexes, which diffuse significantly faster than gold adatoms. With and without chlorine, the lowest activation energy is found for the exchange mechanism. Chlorine furthermore reduces the activation energy for the detachment from kink sites. Kinetic Monte Carlo simulations were performed on the basis of extensive density functional theory calculations. The island-decay rate obtained from these Monte Carlo simulations, as well as the decay rate obtained from the theoretical activation energies and frequency factors when inserted into analytical solutions for Ostwald ripening, are in agreement with experimental island-decay rates in chlorine-containing electrolytes.