We present measurements of the charge state of 0.40- to 0.55-MeV helium ions in earth's outer magnetosphere (L~6) using a novel technique. The radial gradient of the helium ion flux and the east-west anisotropy in the pitch angle distribution are both measured. These are combined with measurements of the magnetic field to calculate the flux-weighted average ion gyroradius. Since the magnitude of the magnetic field and the energies of the ions are known, the gyroradius determines the ion's charge state. During two pairs of geomagnetically quiet days in 1979 we find that most of these ions are singly charged. This result is in accord with theoretical calculations which find that charge exchange reactions between these ions and the neutral hydrogen geocorona are the dominant factor in controlling the charge state of these ions at times longer than a day after their injection. Our results also suggest that the mean charge state of these helium ions may vary with position in the magnetosphere and with time.