A new method for observing the time evolution of phase transitions in highly supercooled, condensed matter is described. It is applicable both to freezing and to transformations between crystalline phases. The molecular clusters to be studied are generated by condensation of vapor expanding supersonically through a Laval nozzle. They are probed downstream by electron diffraction at intervals with a time-of-flight resolution of approximately 1-mu-s. Preliminary results are presented for the freezing of carbon tetrachloride. An induction period is seen before discernible nucleation of the plastically crystalline phase begins at a rate approaching 10(29) m-3 s-1. Nucleation appears to occur in the cooling clusters at very nearly the maximum rate theoretically possible in the liquid before further supercooling renders the liquid too viscid for reasonably facile molecular motion. Results are interpreted in terms of the classical theory of nucleation of Turnbull and Fisher and of Buckle. A value of 4.8(2) mJ/m2 at 175 K is derived for the interfacial free energy of the boundary between the liquid and rhombohedral, plastically crystalline solid. Attention is given to the freezing rates of microdrops exhibiting a distribution in size, to the temperature and its rate of change, to the temperature dependence of viscosity in highly supercooled liquids, and to the slippage in velocity of clusters relative to the expanding gas around them.