  We report the results of high-resolution subpixel imaging of the hard
continuum and Fe K{\alpha} line of the Compton Thick (CT) Active Galactic
Nucleus (AGN) ESO 428-G014, observed with Chandra ACIS. While the 3-4 keV
emission is dominated by an extended component, a single nuclear point source
is prominent in the 4-6 keV range. Instead, two peaks of similar intensity,
separated by ~36 pc in projection on the plane of the sky are detected in the
Fe K{\alpha} emission. The SE knot could be marginally associated with the
heavily obscured hard continuum source. We discuss four possible
interpretations of the nuclear morphology. (1) Given the bolometric luminosity
and likely black hole (BH) mass of ESO 428-G014, we may be imaging two clumps
of the CT obscuring torus in the Fe K{\alpha} line. (2) The Fe K{\alpha} knots
may be connected with the fluorescent emission from the dusty bicone, or (3)
with the light echo of a nuclear outburst. (4) We also explore the less likely
possibility that we may be detecting the rare signature of merging nuclei.
Considering the large-scale kpc-size extent of the hard continuum and Fe
K{\alpha} emission (Papers I and II), we conclude that the AGN in ESO 428-G014
has been active for at least 104 yrs. Comparison with the models of Czerny et
al (2009) suggests high accretion rates during this activity.
