We report the discovery of a luminous quasar, J1007+2115 at $z=7.515$ (P={o}niu={a}ena), from our wide-field reionization-era quasar survey. J1007+2115 is the second quasar now known at $z>7.5$, deep into the reionization epoch. The quasar is powered by a $(1.5pm0.2)times10^9$ $M_{odot}$ supermassive black hole (SMBH), based on its broad MgII emission-line profile from Gemini and Keck near-IR spectroscopy. The SMBH in J1007+2115 is twice as massive as that in quasar J1342+0928 at $z=7.54$, the current quasar redshift record holder. The existence of such a massive SMBH just 700 million years after the Big Bang significantly challenges models of the earliest SMBH growth. Model assumptions of Eddington-limited accretion and a radiative efficiency of 0.1 require a seed black hole of $gtrsim 10^{4}$ $M_{odot}$ at $z=30$. This requirement suggests either a massive black hole seed as a result of direct collapse or earlier periods of rapid black hole growth with hyper-Eddington accretion and/or a low radiative efficiency. We measure the damping wing signature imprinted by neutral hydrogen absorption in the intergalactic medium (IGM) on J1007+2115s Ly$alpha$ line profile, and find that it is weaker than that of J1342+0928 and two other $zgtrsim7$ quasars. We estimate an IGM volume-averaged neutral fraction $langle xrm_{HI}rangle=0.39^{+0.22}_{-0.13}$. This range of values suggests a patchy reionization history toward different IGM sightlines. We detect the 158 $mu$m [C II] emission line in J1007+2115 with ALMA; this line centroid yields a systemic redshift of $z=7.5149pm0.0004$ and indicates a star formation rate of $sim210$ $M_{odot}$ yr$^{-1}$ in its host galaxy.
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