We report the discovery of KELT-4Ab, an inflated, transiting Hot Jupiter orbiting the brightest component of a hierarchical triple stellar system. The host star is an F star with $T_{rm eff}=6206pm75$ K, $log g=4.108pm0.014$, $left[{rm Fe}/{rm H}right]=-0.116_{-0.069}^{+0.065}$, ${rm M_*}=1.201_{-0.061}^{+0.067} {rm M}_{odot}$, and ${rm R_*}=1.610_{-0.068}^{+0.078} {rm R}_{odot}$. The best-fit linear ephemeris is $rm {BJD_{TDB}} = 2456193.29157 pm 0.00021 + Eleft(2.9895936 pm 0.0000048right)$. With a magnitude of $Vsim10$, a planetary radius of $1.699_{-0.045}^{+0.046} {rm R_J}$, and a mass of $0.902_{-0.059}^{+0.060} {rm M_J}$, it is the brightest host among the population of inflated Hot Jupiters ($R_P > 1.5R_J$), making it a valuable discovery for probing the nature of inflated planets. In addition, its existence within a hierarchical triple and its proximity to Earth ($210$ pc) provides a unique opportunity for dynamical studies with continued monitoring with high resolution imaging and precision radial velocities. In particular, the motion of the binary stars around each other and of both stars around the primary star relative to the measured epoch in this work should be detectable when it rises in October 2015.
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