  We examine Chandra observations of the powerful Fanaroff-Riley class II (FR
II) radio galaxy Cygnus A for an X-ray counterpart to the radio transient
Cygnus A-2 that was first detected in 2011. Observations are performed using
the High-Resolution Camera (HRC) instrument in order to spatially resolve
Cygnus A-2 and the central Active Galactic Nucleus (AGN) at a separation of
0.42 arcseconds. Simulated images are generated of the emission region, and
radial profiles for the region of interest are extracted. A comparison between
the simulations and observations reveals no X-ray detection of Cygnus A-2 to a
0.5-7.0 keV flux upper limit of $1.04 \times
10^{-12}\rm\,erg\,cm^{-2}\,s^{-1}$, or a rest-frame 2-10 keV luminosity of
$8.6\times 10^{42}\rm\,erg\,s^{-1}$. We estimate the black hole mass of Cygnus
A-2 based on our X-ray flux limit and find it to be consistent with a flaring
black hole rather than a steadily accreting source. The HRC observations are
additionally compared with archival ACIS data from 2016-2017, and both the
overall morphology and the flux limits of the AGN complex agree between the two
datasets. This consistency is despite the pile-up effect in ACIS which was
previously considered to bias the observed morphology of the AGN. The agreement
between the datasets demonstrates the viability of utilizing the archival
Chandra data of Cygnus A to analyze its AGN at an unprecedented level of
precision.
