Makarov, Keller, Plaxco, and Metiu (MKPM) (to be published) have proposed a model that assumes that the kinetics of protein folding is controlled by the formation of the native contacts. An approximate solution of this model leads to a connection between the rate constant and the number of contacts in the folded state, which agrees with the measurements. In the present article, we perform Kinetic Monte Carlo simulations to test the assumptions and the results of MKPM theory. These simulations require us to know the rate constant for contact formation and dissociation. We show that these can be calculated for the case of a Gaussian chain and then used, in a Kinetic Monte Carlo program, to simulate folding kinetics. It is likely that a Gaussian chain is not a realistic model for the folding of a specific protein. However, it is reasonable to use it to test the assumptions made by MKPM, or by other kinetic models, or to derive generic features of folding rate, such as the dependence on the number of contacts. Another valuable feature of the simulation is that it provides information about the stochastic kinetics of a single chain, which is not yet available experimentally. The simulations find that the probability that a single chain folds at a time t has a maximum, at a time t(m), and decays exponentially for longer times. We show that t(m) is shorter than the time resolution of the experiments and therefore the measurements will conclude that folding is a first-order rate process. This is what is observed experimentally. The folding rate constant produced by simulations agrees with the one obtained by the simplified MKPM theory. Moreover, the simulations were used to test directly some of the assumptions made by MKPM. For example, we show that the free energy of a chain that has made a fair number of contacts can be approximated by a linear function of the number of contacts. The paper also contains two simplified models, which do not assume that the chain is Gaussian but make various mean-field-type assumptions about kinetics. These are tested by simulations and found to be satisfactory.