Timing measurements of Silicon Photomultipliers (SiPM) [1,2] at the picosecond level were performed at Fermilab. The core timing resolution of the electronic measurement technique is approximately 2 ps. The single photoelectron time resolution (SPTR) was measured for the signals coming from the SiPM's. A SPTR of about one hundred picoseconds was obtained for SiPM's illuminated by laser pulses. The dependence of the SPTR on applied bias voltage and on the wavelength of the light was measured. A simple model is proposed to explain the difference in the SPTR for blue and red light. A time of flight system based on the SiPM's, with quartz Cherenkov radiators, was tested in a proton beam at Fermilab. The time resolution obtained is 35 ps per SiPM. Finally, requirements for the SiPM's temperature and bias voltage stability to maintain the time resolution are discussed. Show Partial Abstract