As the size of semiconductor devices decrease, there is an increased interest in understanding the fundamentals of thermal transport at nanoscale features and to predict the properties of semiconductor devices. The Monte Carlo (MC) method, in this case, simulates the transport of phonons within a silicon nanostructure. The Boltzmann Transport Equation (BTE), which dictates the behavior of phonons is solved using the MC method. The model takes into account the phonon dispersion and intrinsic phonon-phonon scattering. The strong temperature and frequency dependent phonon-phonon scattering rate results in accurate results in ballistic, quasi-ballistic, and diffusive phonon transport regimes. The method is validated by calculating and comparing with the thermal conductivity for bulk silicon. This algorithm is employed to nanowires and can be modified to include interface and grain boundary scattering to accurately predict thermal conductivity.