We report a clumpy elongated feature found with deep Chandra Advanced CCD Imaging Spectrometer high-resolution imaging of the Fe K line emission in the nuclear region of the Compton-thick active galactic nucleus galaxy NGC 5643. This feature extends for ∼65 pc north to south (N-S). No corresponding feature is seen in the 3.0-6.0 keV continuum. The Fe K feature is spatially consistent with the N-S elongation found in the CO(2-1) high-resolution imaging with the Atacama Large Millimeter/submillimeter Array, but slightly more extended than the rotating molecular disk of diameter 26 pc indicated by the kinematics of the CO(2-1) line. The Chandra detection of a corresponding north to south structure in the neutral Fe K line would argue for both CO and Fe K emission originating from the obscuring torus.