This paper introduces a 3D stochastic kinetic cellular automaton method for conducting space and time discretized mesoscale simulations of microstructural transformation phenomena such as recovery, recrystallization, and grain growth. The approach is based on discretely solving a classical symmetric rate equation for grain boundary motion at each site of a cubic lattice. The rate equation which is based on an atomic scale diffusion model is turned into a form that is usable for simulations at the mesoscopic scale. The time integration of the underlying differential equations is achieved by Monte Carlo integration. The method is used to simulate recrystallization textures and microstructures.