We present a powerful kinetic Monte Carlo (KMC) algorithm that allows one to simulate the growth of nanocrystalline silicon by plasma enhanced chemical vapor deposition (PECVD) for film thicknesses as large as several hundreds of monolayers. Our method combines a standard n-fold KMC algorithm with an efficient Markovian random walk scheme accounting for the surface diffusive processes of the species involved in PECVD. These processes are extremely fast compared to chemical reactions, thus in a brute application of the KMC method more than 99% of the computational time is spent in monitoring them. Our method decouples the treatment of these events from the rest of the reactions in a systematic way, thereby dramatically increasing the efficiency of the corresponding KMC algorithm. It is also making use of a very rich kinetic model which includes 5 species (H, SiH3, SiH2, SiH, and Si2H5) that participate in 29 reactions. We have applied the new method in simulations of silicon growth under several conditions (in particular, silane fraction in the gas mixture), including those usually realized in actual PECVD technologies. This has allowed us to directly compare against available experimental data for the growth rate, the mesoscale morphology, and the chemical composition of the deposited film as a function of dilution ratio.