We present "on-the-fly," fully sampled maps of CO(1-0) in the central 15' o
f the spiral galaxy IC 342. In addition to the bright CO nuclear peak, ther
e is a prominent CO 2'x5' bar and an extensive CO disk. The bar and nucleus
contain 30% of the total observed CO emission in IC 342. Beyond the bar th
e CO disk contains two spiral arms, which coincide with the two inner optic
al arms. The substantial inter-arm CO component within this inner region ha
s a mean surface density of 8 M-. pc(-2), close to the mean surface density
of 10 M-. pc(-2), that extends to a radius of 7' (4 kpc). The total inferr
ed H-2 mass is 7 x 10(8) M-. which is 30% of the total H I mass. We combine
the CO data with VLA H I maps to obtain a map of the total gas surface den
sity (Sigma (HI) + Sigma (H2)) in IC 342. The gas surface density shows a c
entrally peaked disk, dominated by H-2 to a radius of 5' (3 kpc). Spiral ar
ms run continuously from the inner to outer galaxy, transitioning smoothly
from predominantly molecular in the inner galaxy to predominantly atomic at
large radii. On a global scale, the gas surface density is spatially corre
lated with optical spiral arm structure. On 1' (600 pc) scales the disk dis
plays bar and arm asymmetries, azimuthal displacements of CO and H I emissi
on, and structure that becomes increasingly complex with increasing galacti
c radii. We find an excellent correlation between 21 cm radio continuum and
the total gas surface density.