We have obtained high resolution (2.9″∼260 pc) aperture synthesis imaging of NGC 1068 in the CO J = 1 → 0 line made with the Owens Valley mm Interferometer. The major features seen in CO are: (1) the inner spiral arms of molecular gas at ∼15″ radius (1.5 kpc) which originate from the ends of the central stellar bar, and (2) a compact source (∼3″) coincident with the Seyfert 2 nucleus. The components within 2 kpc of the galactic nucleus account for approximately 30% of the total molecular gas content in NGC 1068. The spiral arm CO emission is resolved into 38 discrete complexes which closely correlate with regions of strong Hα and 10 μm emission. The sizes of these structures range up to 500 pc and their masses derived from the CO line flux are 2×107−7×10 M⊙. Somewhat smaller mass estimates are obtained from the virial theorem using the observed CO linewidths and sizes, suggesting that these complexes may be self-gravitating.