A rare signal was detected at 23:53 Moscow time on April 27, 1986 with the LSD low-background scintillation detector located under Mont Blanc at a distance of 1820 km from Chernobyl. To reveal the origin of this signal, we discuss the results obtained with other instruments operating within a similar program, as well as analyze the characteristics of the pulses of the signal and facts referring to the explosion of the Chernobyl reactor. A hypothesis based on detection with the LSD of gamma-quanta from β decays of 135I nuclei ejected into atmosphere by the reactor explosion and carried in the underground detector camera with air of positive ventilation is considered. The explosion origin of the LSD signal indicates a new technogenic source of the background in the search for neutrino bursts from cores of collapsing stars.