A number of extragalactic radio sources which exhibit symmetric jets on parsec scales have now been found to have neutral hydrogen absorption at or near the systemic velocities of their host galaxies. Understanding the spatial distribution and kinematics of the HI detected toward the central parsecs of these sources provides an important test of unified schemes for AGN. We present results of Global VLBI Network observations of the redshifted 21 cm HI line toward the Compact Symmetric Object 1946+708 (z=0.101). We find significant structure in the gas on parsec scales. The peak column density of the HI (N_HI~3x10^23 cm^-2(Ts/8000K)) occurs near the center of activity of the source, as does the highest velocity dispersion (FWHM 350 to 400 km/s). There is also good evidence for a torus of ionized gas with column density 7x10^22 cm^-2}. The jets in 1946+708 exhibit bi-directional motion measurable on timescales of a few years. The resulting unique information about the geometry of the continuum source greatly assists in the interpretation of the gas distribution, which is strongly suggestive of a circumnuclear torus of neutral atomic and ionized material with one or more additional compact clumps of gas along the line of sight to the approaching jet.