The detection of 200-1000 MeV neutrons requires large amounts, ∼100 cm, of detector material because of the long nuclear interaction length of these particles. In the example of the NeuLAND neutron time-of-flight detector at FAIR, this is accomplished by using 3000 monolithic scintillator bars of 270×5×5 cm 3 size made of a fast plastic. Each bar is read out on the two long ends, and the needed time resolution of σ t < 150 ps is reached with fast timing photomultipliers. In the present work, it is investigated whether silicon photomultiplier (SiPM) photosensors can be used instead. Experiments with a picosecond laser system were conducted to determine the timing response of the assembly made up of SiPM and preamplifier. The response of the full system including also the scintillator was studied using 30 MeV single electrons provided by the ELBE superconducting electron linac. The ELBE data were matched by a simple Monte Carlo simulation, and they were found to obey an inverse-square-root scaling law. In the electron beam tests, a time resolution of σ t = 136 ps was reached with a pure SiPM readout, well within the design parameters for NeuLAND.