  Quasars are the most luminous non-transient objects known and as a result
they enable studies of the Universe at the earliest cosmic epochs. Despite
extensive efforts, however, the quasar ULAS J1120+0641 at z=7.09 has remained
the only one known at z>7 for more than half a decade. Here we report
observations of the quasar ULAS J134208.10+092838.61 (hereafter J1342+0928) at
redshift z=7.54. This quasar has a bolometric luminosity of 4e13 times the
luminosity of the Sun and a black hole mass of 8e8 solar masses. The existence
of this supermassive black hole when the Universe was only 690 million years
old---just five percent of its current age---reinforces models of early
black-hole growth that allow black holes with initial masses of more than about
1e4 solar masses or episodic hyper-Eddington accretion. We see strong evidence
of absorption of the spectrum of the quasar redwards of the Lyman alpha
emission line (the Gunn-Peterson damping wing), as would be expected if a
significant amount (more than 10 per cent) of the hydrogen in the intergalactic
medium surrounding J1342+0928 is neutral. We derive a significant fraction of
neutral hydrogen, although the exact fraction depends on the modelling.
However, even in our most conservative analysis we find a fraction of more than
0.33 (0.11) at 68 per cent (95 per cent) probability, indicating that we are
probing well within the reionization epoch of the Universe.
