As previously demonstrated, an excellent timing resolution below 100ps FWHM is possible in time-of-flight positron emission tomography (TOF PET) if the detection method is based on the principle of detecting photons of Cherenkov light, produced in a suitable material and detected by microchannel plate photomultipliers (MCP PMTs). In this work, the silicon photomultipliers (SiPMs) were tested for the first time as the photodetectors in Cherenkov TOF PET. The high photon detection efficiency (PDE) of SiPMs led to a large improvement in detection efficiency. On the other hand, the time response of currently available SiPMs is not as good as that of MCP PMTs. The SiPM dark counts introduce a new source of random coincidences in Cherenkov method, which would be overwhelming with present SiPM technology at room temperature. When the apparatus was cooled, its performance significantly improved.