Emission in the hydrogen recombination line H53-alpha has been detected, for the first time, in another galaxy: the nearby starburst system M82. This line is produced primarily by spontaneous emission and provides the most direct, extinction-independent estimate of the ionization rate in the star-forming complex. The line strength implies an ionization rate of 1.1 x 10 to the 54th/s, approximately five times larger than that inferred from Br-alpha observations, and indicates a dust extinction at 4 microns of more than 1 mag. Comparison of the 3.3 mm free-free continuum and H53-alpha fluxes implies an average electron temperature of about 5000 K. Analysis of the line excitation conditions, using the H53-alpha emission in conjunction with that in the far-IR O(2+) and N(2+) forbidden lines, together with the IR luminosity, suggests that only a very restricted range of stellar masses are formed. 41 refs.