An experimental method is described for studying the combustion of a stationary unsupported fuel droplet in a stagnant ambience under very low gravity. A unique feature of the method is that of being able to observe the droplet burning history over the entire period from ignition to extinction or complete burning. The procedure consisted of propelling a droplet from a piezoelectric generator in a near vertical trajectory and then releasing the chamber within which the droplet was introduced, as well as associated instrumentation, into free fall when the droplet reached the apex of its trajectory. Results with the technique are described for toluene and heptane droplets. A phenomenon believed to be indicative of extinction was observed for an unsupported heptane droplet, whereas the evidence for extinction of toluene was less clear. Measured burning rates were in good agreement with both early theories that have assumed spherically symmetric combustion, and with prior limited experiments on heptane droplets obtained under low gravity that, however, were capable of recording a more limited fraction of the total burning history.