  We present 1.4 pc resolution observations of 256 GHz nuclear radio continuum
and HCN ($J=3 \to 2$) in the molecular torus of NGC 1068. The integrated radio
continuum emission has a flat spectrum consistent with free-free emission and
resolves into an X-shaped structure resembling an edge-brightened bicone. HCN
is detected in absorption against the continuum, and the absorption spectrum
shows a pronounced blue wing that suggests a high-velocity molecular outflow
with speeds reaching 450 km/s. Analysis of the off-nucleus emission line
kinematics and morphology reveals two nested, rotating disk components. The
inner disk, inside $r\sim 1.2$ pc, has kinematics consistent with the nearly
edge-on, geometrically thin water megamaser disk in Keplerian rotation around a
central mass of $1.66\times 10^7\,\mbox{M}_\odot$. The outer disk, which
extends to $\sim 7$~pc radius, counter-rotates relative to the inner disk. The
rotation curve of the outer disk is consistent with rotation around the same
central mass as the megamaser disk but in the opposite sense. The morphology of
the molecular gas is asymmetric around the nuclear continuum source. We
speculate that the outer disk formed from more recently introduced molecular
gas falling out of the host galaxy or from a captured dwarf satellite galaxy.
In NGC 1068, we find direct evidence that the molecular torus consists of
counter-rotating and misaligned disks on parsec scales.
