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: {M}{{gas}}{{torus}}=(1+/- 0.3)× {10}5 {M}ȯ 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.