We compare the solar modulation of galactic cosmic ray helium and electrons at 1 AU, within the 600- to 1000-MV magnetic rigidity interval, during a period covering 20 years, from the solar minimum of 1965 through 1984. Most of the data were obtained by University of Chicago cosmic ray telescopes on board balloons and the IMP series and ISEE 3 satellites. Comparison of the time-intensity variations during the two solar maxima around 1970 and 1981 shows that after 1970 the intensity of helium recovers earlier than that of the electrons, whereas after 1981 the intensity of electrons recovers earlier than that of helium. Within the measured magnetic rigidity interval the flux ratio of helium to electrons (He/e) undergoes a major increase during 1969-1971 and a major decrease during 1979-1983, periods that include the times of reversal of the polarity of the solar polar magnetic fields. A conventional model of solar modulation can describe the modulation of protons and helium from 1965 through 1984, but its predictions depart significantly from the observed modulation of electrons around and after the 1981 solar maximum. The difference in particle velocity between nuclei and electrons in the rigidity interval under study cannot alone account for the observations. The above experimental findings are consistent with a dependence of the solar modulation of galactic cosmic rays on the sign of the particle charge.