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 redshift 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 4 × 10¹³ times the luminosity of the Sun and a black-hole mass of 8 × 10⁸ solar masses. The existence of this supermassive black hole when the Universe was only 690 million years old-just five per cent of its current age-reinforces models of early black-hole growth that allow black holes with initial masses of more than about 10⁴ solar masses or episodic hyper-Eddington accretion. We see strong evidence of absorption of the spectrum of the quasar redwards of the Lyman α 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 such 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.