So far, roughly 40 quasars with redshifts greater than z = 6 have been discovered1-8. Each quasar contains a black hole with a mass of about one billion solar masses (109)2,6,7,9-13. The existence of such black holes when the Universe was less than one billion years old presents substantial challenges to theories of the formation and growth of black holes and the coevolution of black holes and galaxies14. Here we report the discovery of an ultraluminous quasar, SDSS J010013.02+280225.8, at redshift z = 6.30. It has an optical and near-infrared luminosity a few times greater than those of previously known z > 6 quasars. On the basis of the deep absorption trough on the blue side of the Lyman-emission line in the spectrum, we estimate the proper size of the ionized proximity zone associated with the quasar to be about 26 million light years, larger than found with other z > 6.1 quasars with lower luminosities16. We estimate (on the basis of a near-infrared spectrum) that the black hole has a mass of ∼1.2 × 1010, which is consistent with the 1.3 × 1010 derived by assuming an Eddington-limited accretion rate.