  We present new interferometer observations of the 12CO(1-0) and 12CO(2-1)
line emission of NGC 1068 with a resolution of 0.7''. The molecular gas in the
inner 5'' is resolved into a ring with two bright knots east and west of the
nuclear continuum emission. For the first time in NGC 1068, we can trace
molecular gas at ~0.18'' (13pc) from the nucleus. The high velocities in this
region imply an enclosed mass of ~10^8 M_solar. This value is consistent with a
black hole mass of 1.7x10^7 M_solar plus a contribution from a compact nuclear
stellar cluster. Perpendicular to the kinematic major axis optical images of
NGC1068 show a bright, stellar, oval structure of eccentricity 0.8 and a
deprojected length of 17kpc. Analysis of the rotation curve shows the CO spiral
arms are at the inner Lindblad resonance of this bar-like structure. Inside the
molecular spiral arms the CO kinematic axis changes direction probably in
response to the 2.5kpc (deprojected) long stellar bar seen in the near infrared
(NIR). The low velocity dispersion indicates the molecular gas is in a disk
with a thickness of 10pc in the nuclear region and 100pc in the spiral arms.
  We constructed kinematic models for the molecular gas using elliptical orbits
caused by a ~1'' nuclear bar and using tilted rings resulting in a warp. We
find that the gas motions are consistent with either the warp or the bar
models. However, because there is no evidence for a 1'' nuclear bar in NIR
images, we favor the warp model. A warped CO disk can also explain the
obscuration of the AGN, the extinction of light from the nuclear stellar
cluster, and the observed NIR and mid-IR polarization. The model predicts the
warped CO disk should become edge-on at a radius of 70pc, thereby creating a
cavity for the ionization cone.
