  We present the discovery of KELT-21b, a hot Jupiter transiting the $V=10.5$
A8V star HD 332124. The planet has an orbital period of
$P=3.6127647\pm0.0000033$ days and a radius of $1.586_{-0.040}^{+0.039}$ $R_J$.
We set an upper limit on the planetary mass of $M_P<3.91$ $M_J$ at $3\sigma$
confidence. We confirmed the planetary nature of the transiting companion using
this mass limit and Doppler tomographic observations to verify that the
companion transits HD 332124. These data also demonstrate that the planetary
orbit is well-aligned with the stellar spin, with a sky-projected spin-orbit
misalignment of $\lambda=-5.6_{-1.9}^{+1.7 \circ}$. The star has
$T_{\mathrm{eff}}=7598_{-84}^{+81}$ K, $M_*=1.458_{-0.028}^{+0.029}$
$M_{\odot}$, $R_*=1.638\pm0.034$ $R_{\odot}$, and $v\sin I_*=146$ km s$^{-1}$,
the highest projected rotation velocity of any star known to host a transiting
hot Jupiter. The star also appears to be somewhat metal-poor and
$\alpha$-enhanced, with [Fe/H]$=-0.405_{-0.033}^{+0.032}$ and
[$\alpha$/Fe]$=0.145 \pm 0.053$; these abundances are unusual, but not
extraordinary, for a young star with thin-disk kinematics like KELT-21.
High-resolution imaging observations revealed the presence of a pair of stellar
companions to KELT-21, located at a separation of 1.2" and with a combined
contrast of $\Delta K_S=6.39 \pm 0.06$ with respect to the primary. Although
these companions are most likely physically associated with KELT-21, we cannot
confirm this with our current data. If associated, the candidate companions
KELT-21 B and C would each have masses of $\sim0.12$ $M_{\odot}$, a projected
mutual separation of $\sim20$ AU, and a projected separation of $\sim500$ AU
from KELT-21. KELT-21b may be one of only a handful of known transiting planets
in hierarchical triple stellar systems.
