  The discovery of hundreds of QSOs in the first Gyr of the Universe powered by
already grown SMBHs challenges our knowledge of SMBH formation. In particular,
investigations of $z>6$ QSOs presenting notable properties can provide unique
information on the physics of fast SMBH growth in the early universe. We
present the results of follow-up observations of the $z=6.515$ radio-quiet QSO
PSO167-13, which is interacting with a close companion galaxy. The PSO167-13
system has been recently proposed to host the first heavily obscured X-ray
source at high redshift. We observed PSO167-13 with Chandra/ACIS-S (177 ks),
and obtained new spectroscopic observations (7.2 h) with Magellan/FIRE. No
significant X-ray emission is detected from the PSO167-13 system, suggesting
that the obscured X-ray source previously tentatively detected was either due
to a strong background fluctuation or is highly variable. The upper limit (90%
confidence level) on the X-ray emission of PSO167-13
($L_{2-10\,\mathrm{keV}}<8.3\times10^{43}\,\mathrm{erg s^{-1}}$) is the lowest
available for a $z>6$ QSO. The ratio between the X-ray and UV luminosity of
$\alpha_{ox}<-1.95$ makes PSO167-13 a strong outlier from the
$\alpha_{ox}-L_{UV}$ and $L_X-L_{\mathrm{bol}}$ relations. In particular, its
X-ray emission is $>6$ times weaker than the expectation based on its UV
luminosity. The new Magellan/FIRE spectrum of PSO167-13 is strongly affected by
the unfavorable sky conditions, but the tentatively detected C IV and Mg II
emission lines appear strongly blueshifted. The most plausible explanations for
the X-ray weakness of PSO167-13 are intrinsic weakness or small-scale
absorption by Compton-thick material. The possible strong blueshift of its
emission lines hints at the presence of nuclear winds, which could be related
to its X-ray weakness.
