Recent developments in positron trapping technology have made possible experimentation with dense interacting positronium gases. Along with these capabilities comes a need for suitable measurement techniques, and accordingly we have developed a method to measure positronium lifetimes from a single intense burst of positrons. Our method is based on recording the anode signal from a photomultiplier with a fast oscilloscope following a short-time positron burst which allows us to measure transitory effects as well as high density positronium interactions.