We report a clumpy elongated feature found with deep Chandra ACIS high-resolution imaging of the Fe K{alpha} line emission in the nuclear region of the Compton Thick Active Galactic Nucleus (CT AGN) galaxy NGC 5643. This feature extends for ~65 pc N-S. No corresponding feature is seen in the 3.0-6.0 keV continuum. The Fe K{alpha} feature is spatially consistent with the N-S elongation found in the CO(2-1) high resolution imaging with ALMA (Alonso-Herrero et al 2018), but slightly more extended than the rotating molecular disk of r=26 pc indicated by the kinematics of the CO(2-1) line. The Chandra detection of a corresponding N-S structure in the neutral Fe K{alpha} line, would argue for both CO and Fe K{alpha} emission originating from the obscuring torus.