  We report X-ray observations of the most distant known gravitationally lensed
quasar, J0439+1634 at $z=6.52$, which is also a broad absorption line (BAL)
quasar, using the XMM-Newton Observatory. With a 130 ks exposure, the quasar is
significantly detected as a point source at the optical position with a total
of 358$^{+19}_{-19}$ net counts using the EPIC instrument. By fitting a
power-law plus Galactic absorption model to the observed spectra, we obtain a
spectral slope of $\Gamma=1.45^{+0.10}_{-0.09}$. The derived optical-to-X-ray
spectral slope $\alpha_{\rm{ox}}$ is $-2.07^{+0.01}_{-0.01}$, suggesting that
the X-ray emission of J0439+1634 is weaker by a factor of 18 than the
expectation based on its 2500 Angstrom luminosity and the average
$\alpha_{\rm{ox}}$ vs. luminosity relationship. This is the first time that an
X-ray weak BAL quasar at $z>6$ has been observed spectroscopically. Its X-ray
weakness is consistent with the properties of BAL quasars at lower redshift. By
fitting a model including an intrinsic absorption component, we obtain
intrinsic column densities of
$N_{\rm{H}}=2.8^{+0.7}_{-0.6}\times10^{23}\,\rm{cm}^{-2}$ and $N_{\rm{H}}=
4.3^{+1.8}_{-1.5}\times10^{23}\,\rm{cm}^{-2}$, assuming a fixed $\Gamma$ of 1.9
and a free $\Gamma$, respectively. The intrinsic rest-frame 2--10 keV
luminosity is derived as $(9.4-15.1)\times10^{43}\,\rm{erg\,s}^{-1}$, after
correcting for lensing magnification ($\mu=51.3$). The absorbed power-law model
fitting indicates that J0439+1634 is the highest redshift obscured quasar with
a direct measurement of the absorbing column density. The intrinsic high column
density absorption can reduce the X-ray luminosity by a factor of $3-7$, which
also indicates that this quasar could be a candidate of intrinsically X-ray
weak quasar.
