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We present deep Chandra observations of PSO J231.6576$-$20.8335, a quasar atredshift z=6.59 with a nearby (${\sim}8$ proper kpc) companion galaxy. ALMAobserved both the quasar and companion to be bright in [C II], and the systemhas significant extended Ly$\alpha$ emission around the quasar, suggesting thata galaxy merger is ongoing. Unlike previous studies of two similar systems, anddespite observing the system with Chandra for 140 ks, we do not detect thecompanion 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 $\Gamma=2.6^{+1.0}_{-0.9}$), whichresults 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 twopossible 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 quasarhas a more normal spectrum ($\Gamma{\sim}2$) but is therefore less X-rayluminous ($L_{2-10} \sim 0.6 \times 10^{45}\ \textrm{ erg}\ \textrm{ s}^{-1}$).

X-ray Observations of a [C II]-bright, z=6.59 Quasar/Companion System