  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 $(1.5\pm0.2)\times10^9$
$M_{\odot}$ 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+2115's Ly$\alpha$ line profile, and
find that it is weaker than that of J1342+0928 and two other $z\gtrsim7$
quasars. We estimate an IGM volume-averaged neutral fraction $\langle
x\rm_{HI}\rangle=0.39^{+0.22}_{-0.13}$. 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 $z=7.5149\pm0.0004$ and indicates a star formation rate of
$\sim210$ $M_{\odot}$ yr$^{-1}$ in its host galaxy.
