We present results of a kinetic Monte Carlo simulation of low-pressure diamond film growth from a C[111] substrate via acetylene and hydrogen vapor deposition. Interactions are governed by a semiempirical interatomic potential-energy function. We find that acetylene binding to a clean C[111] surface is favored in this Monte Carlo process, but adsorption of a second ${\mathrm{C}}_{2}$${\mathrm{H}}_{2}$ is not likely until the neighborhood around the site for the second-layer adsorption contains a sufficient number of first-layer adsorbed molecules. This property of the potential energy is responsible for layer-by-layer growth of the film. We also find that the simulated surface is somewhat rougher than diamond surfaces studied by atomic force microscopy. This suggests a need to include the methyl radical in future simulation models.