  We present deep Chandra observations of PSO J231.6576$-$20.8335, a quasar at
redshift z=6.59 with a nearby (${\sim}8$ proper kpc) companion galaxy. ALMA
observed both the quasar and companion to be bright in [C II], and the system
has significant extended Ly$\alpha$ emission around the quasar, suggesting that
a galaxy merger is ongoing. Unlike previous studies of two similar systems, and
despite observing the system with Chandra for 140 ks, we do not detect the
companion in X-rays. The quasar itself is detected, but only
$13.3^{+4.8}_{-3.7}$ net counts are observed. From a basic spectral analysis,
the X-ray spectrum of the quasar is soft (hardness ratio of $\mathcal{HR} =
-0.60_{-0.27}^{+0.17}$, power-law index of $\Gamma=2.6^{+1.0}_{-0.9}$), which
results in a rest-frame X-ray luminosity comparable to other bright quasars
($L_{2-10} = 1.09^{+2.20}_{-0.70}\times 10^{45}\ \textrm{erg}\
\textrm{s}^{-1}$) despite the faint observed X-ray flux. We highlight two
possible interpretations of this result: the quasar has a steep value of
$\Gamma$ -- potentially related to observed ongoing Eddington accretion --
thereby pushing much of the emission out of our observed band, or the quasar
has a more normal spectrum ($\Gamma{\sim}2$) but is therefore less X-ray
luminous ($L_{2-10} \sim 0.6 \times 10^{45}\ \textrm{ erg}\ \textrm{ s}^{-1}$).
