Statistically significant variations have been observed in the differential flux of ~27-MeV anomalous cosmic ray (ACR) oxygen, helium, and protons at the Voyager 1 spacecraft during 1998 and 1999 (at a helioradius of ~73 AU). The quasiperiodic variations are in phase, with oxygen and helium having periods near 151 days, while protons exhibit a period of ~146 days. The Voyager 1 ACRs vary by ~30% with respect to the trend, and similar galactic cosmic ray variations, if they exist, must be less than ~5%, probably much less. No similar, significant periodicities have been detected for these same ACR species at Voyager 2 (at 57 AU) during this period. We report on these and other periodicities in the Voyager Low Energy Charged Particle experiment measurements and address the possible connection between this ~151-day ACR periodicity and the previously discovered ~154-day periodicities in solar flares, the interplanetary magnetic field, and other phenomena. ¿ 2001 American Geophysical Union