We used the Atacama Large Millimeter Array (ALMA) to map the emission of the CO(6-5) molecular line and the 432 μm continuum emission from the 300 pc sized circumnuclear disk (CND) of the nearby Seyfert 2 galaxy NGC 1068 with a spatial resolution of ∼4 pc. These observations spatially resolve the CND and, for the first time, image the dust emission, the molecular gas distribution, and the kinematics from a 7-10 pc diameter disk that represents the submillimeter counterpart of the putative torus of NGC 1068. We fitted the nuclear spectral energy distribution of the torus using ALMA and near- and mid-infrared (NIR/MIR) data with CLUMPY torus models. The mass and radius of the best-fit solution for the torus are both consistent with the values derived from the ALMA data alone: and R torus = 3.5 ± 0.5 pc. The dynamics of the molecular gas in the torus show strong non-circular motions and enhanced turbulence superposed on a surprisingly slow rotation pattern of the disk. By contrast with the nearly edge-on orientation of the H2O megamaser disk, we found evidence suggesting that the molecular torus is less inclined (i = 34°-66°) at larger radii. The lopsided morphology and complex kinematics of the torus could be the signature of the Papaloizou-Pringle instability, long predicted to likely drive the dynamical evolution of active galactic nuclei tori.