The helium abundance in the Jovian atmosphere has been determined by a new method from our observations of the occultation of beta Scorpii by Jupiter. The occultation light curves, consisting of simultaneous records at three wavelengths with a time resolution of 0.01 sec, are dominated by sharp, well-defined intensity peaks or spikes. Because of the wavelength-dependence of the refractivity of the Jovian atmosphere, the arrival time of a given spike at the Earth is also wavelength dependent. A new method for determining the composition of a hydrogen-helium atmosphere from such data is presented, and the principal sources of error are discussed and evaluated.