The results of searching for neutrino events from the blazar PKS 0735+17 at the Baksan Underground Scintillation Telescope (BUST) are presented. A neutrino from the PKS 0735+17 region was detected at BUST on December 4, 2021, during a strong outburst of this object, coinciding with an observed Fermi LAT gamma-ray outburst. The BUST neutrino event preceded the detections of high-energy neutrino events from the PKS 0735+17 region by IceCube, Baikal-GVD, and KM3NeT.