  We present X-ray imaging and spectroscopy of the redshift z=7.084 radio-quiet
quasar ULAS J112001.48+064124.3 obtained with Chandra and XMM-Newton. The
quasar is detected as a point source with both observatories. The Chandra
observation provides a precise position, confirming the association of the
X-ray source and the quasar, while a sufficient number of photons is detected
in the XMM-Newton observation to yield a meaningful X-ray spectrum. In the
XMM-Newton observation the quasar has a 2-10 keV luminosity of 4.7+-0.9 times
10^44 erg/s and a spectral slope alpha = 1.6+0.4/-0.3 (where f_nu is
proportional to nu^-alpha). The quasar appears to have dimmed in the 15 months
between the two observations, with a 2-10 keV luminosity of $1.8+1.0/-0.7 times
10^45 erg/s during the Chandra observation. We derive optical to X-ray spectral
slopes alpha_OX of 1.76+-0.07 and 1.54+0.09/-0.08 at the times of the
XMM-Newton and Chandra observations respectively, consistent with the range of
alpha_OX found in other quasars of comparable ultraviolet luminosity. The very
soft X-ray spectrum suggests that the quasar is accreting above the Eddington
rate, L/L_Edd = 5+15/-4, compared to L/L_Edd = 1.2+0.6/-0.5 derived from the
rest-frame ultraviolet. Super-Eddington accretion would help to reduce the
discrepancy between the age of the quasar implied by the small size of the
ionized near zone in which it sits (<10^7 years), and the characteristic
e-folding time (2.5 times 10^7 years if L/L_Edd=2). Such super-Eddington
accretion would also alleviate the challenging constraints on the seed black
hole mass provided that the quasar has been rapidly accreting throughout its
history. The remnant of an individual population III star is a plausible
progenitor if an average L/L_Edd>1.46 has been maintained over the quasar's
lifetime.
