Models for energy storage in the solar corona due to the twisting of coronal magnetic fields by subphotospheric flows imply that coronal currents should be neutralized (i.e., observed currents over a given polarity of the magnetic field should sum to zero). The neutralized current hypothesis is quantitatively tested by examining vector magnetic field data from 21 active regions observed by the Solar Magnetic Field Telescope of the Huairou Solar Observing Station of Beijing Astronomical Observatory. For each active region, the current over the positive polarity of the field, I+, is estimated, as well as the current over the negative polarity, I-, and the total current over both polarities, Itot. In no case is the total current Itot significantly different from zero. The currents I+ and I- are found to be significantly different from zero (at the 3 σ level) in more than half of the active regions studied, implying that large-scale currents in active regions are typically unneutralized. The implications of this result and the relationship of this study to related studies (e.g., of current helicity) are discussed.