We have used Raman spectroscopy to study indium nitride thin films grown by molecular beam epitaxy on (111) silicon substrates at temperatures between 450 and 550 C. The Raman spectra show well defined peaks at 443, 475, 491, and 591 cm{-1}, which correspond to the A_1(TO), E_1(TO), E_2^{high}, and A_1(LO) phonons of the wurtzite structure, respectively. In backscattering normal to the surface the A_1(TO) and E_1(TO) peaks are very weak, indicating that the films grow along the hexagonal c axis. The dependence of the peak width on growth temperature reveals that the optimum temperature is 500 C, for which the fullwidth of the E_2^{high} peak has the minimum value of 7 cm{-1}. This small value, comparable to previous results for InN films grown on sapphire, is evidence of the good crystallinity of the films.