We have developed a novel photofragment spectrometer to investigate the fragmentation of neutral molecules into two, three, and more neutral fragments. The parent molecules are laser prepared in a fast beam. The photofragments are detected in coincidence by a time- and position-sensitive detector which consists of multichannel plates and delay line anodes. We have developed new electronic pulse routers which allow us to measure consecutive fragment hits with dead times as low as a few nanoseconds. A new algorithm has been developed to determine for each triple hit the momentum vectors of the three fragments from the measured arrival time differences and positions. To demonstrate the performance of the spectrometer, we have investigated two- and three-body decay processes of laser-prepared triatomic hydrogen molecules H-3 into H+H-2 fragment pairs as well as into three hydrogen atoms H(1s)+H(1s)+H(1s). For two-body decay of vibrationless H-3 3s(2)A(1)'(N=1, K=0), we have found that the resolution in the kinetic energy release spectra is far better than that achieved in previous investigations. With the new spectrometer, kinematically complete investigations of the breakup of a neutral molecule into three neutral fragments have been performed. The final state distributions in the three body decay of laser-prepared H-3 molecules show pronounced structures which give insight into the complex molecular decay mechanisms. (C) 2000 American Institute of Physics. [S0034-6748(00)02111-0].