  While theoretical arguments predict that most of the early growth of
supermassive black holes (SMBHs) happened during heavily obscured phases of
accretion, current methods used for selecting $z>6$ quasars (QSOs) are strongly
biased against obscured QSOs, thus considerably limiting our understanding of
accreting SMBHs during the first Gyr of the Universe from an observational
point of view. We report the $Chandra$ discovery of the first heavily obscured
QSO candidate in the early universe, hosted by a close ($\approx5$ kpc) galaxy
pair at $z=6.515$. One of the members is an optically classified type 1 QSO,
PSO167-13. The companion galaxy was first detected as a [C II] emitter by ALMA.
An X-ray source is significantly ($P=0.9996$) detected by $Chandra$ in the 2-5
keV band, with $<1.14$ net counts in the 0.5-2 keV band, although the current
positional uncertainty does not allow a conclusive association with either
PSO167-13 or its companion galaxy. From X-ray photometry and hardness-ratio
arguments, we estimated an obscuring column density of
$N_H>2\times10^{24}\,\mathrm{cm^{-2}}$ and
$N_H>6\times10^{23}\,\mathrm{cm^{-2}}$ at $68\%$ and $90\%$ confidence levels,
respectively. Thus, regardless of which of the two galaxies is associated with
the X-ray emission, this source is the first heavily obscured QSO candidate at
$z>6$.
