  We present high-resolution CO, HCN, and 13CO maps of the inner arcminute of
NGC 1068 made with the BIMA interferometer. Several features appear in the CO
map which have not previously been observed: (1) a firm detection of CO line
emission from a compact region centered on the nucleus of the galaxy; (2) the
detection of a triplet velocity structure characteristic of kinematically
independent regions shown on the spectrum of the unresolved nuclear emission ;
and (3) the detection of a molecular bar, the extent and position angle of
which are in good agreement with the 2 $\mu$m stellar bar. The most intense CO
emission is nonnuclear; the structure and kinematics of this emission imply
that this gas is distributed along the inner spiral arms and not in a ring. The
bar's kinematic influence on the molecular gas in the spiral arms is modest,
with typical ordered noncircular motions of \la\ 30 \kms\ in the plane of the
galaxy. Interior to the spiral arms, the bar's influence is more dramatic, as
reflected by the twisted isovelocity contours in the CO and HCN velocity
fields. The surface density of molecular gas within the central 100 pc radius
of NGC 1068 is the same as that in the central 200 pc radius in the Milky Way
to within the uncertainties. There is evidence for an $m= 1$ kinematic mode in
NGC 1068; we find the kinematic center of rotation to be displaced from the
radio continuum center by about 2.9", or 200 pc. The HCN image, in contrast to
the CO map, shows a strong concentration of emission centered on the nucleus.
The ratio of integrated intensities of the HCN emission to that of CO is about
0.6 and is the highest ratio measured in the central region of any galaxy.
