Si solid state photomultipliers utilize impact ionization of shallow impurity donor levels to create an avalanche multiplication when triggered by a photoexcited hole. The distribution of pulse height from a single photon detection event shows narrow dispersion, which implies that the avalanche multiplication process in these devices is inherently noise-free. We have measured the excess noise factor using two different techniques, digital pulse height analysis and analog noise power measurement. The results demonstrate nearly noise-free avalanche multiplication accomplished in these devices.