Authors:Stevens et alAbstract:We report the discovery of KELT-12b, a highly inflated Jupiter-mass planet transiting a mildly evolved host star. We identified the initial transit signal in the KELT-North survey data and established the planetary nature of the companion through precise follow-up photometry, high-resolution spectroscopy, precise radial velocity measurements, and high-resolution adaptive optics imaging. Our preferred best-fit model indicates that the V=10.64 host, TYC 2619-1057-1, has Teff=6278±51 K, logg⋆=3.89+0.054−0.051, and [Fe/H] = 0.19+0.083−0.085, with an inferred mass M⋆=1.59+0.071−0.091M⊙ and radius R⋆=2.37±0.18R⊙. The planetary companion has MP=0.95±0.14MJ, RP=1.79+0.18−0.17RJ, loggP=2.87+0.097−0.098, and density ρP=0.21+0.075−0.054 g cm−3, making it one of the most inflated giant planets known. The time of inferior conjunction in BJDTDB is 2457088.692055±0.0009 and the period is P=5.0316144±0.0000306 days. Despite the relatively large separation of ∼0.07 AU implied by its ∼5.03-day orbital period, KELT-12b receives significant flux of 2.93+0.33−0.30×109 erg s−1 cm−2 from its host. We compare the radii and insolations of transiting giant planets around hot (Teff≥6250 K) and cool stars, noting that the observed paucity of known transiting giants around hot stars with low insolation is likely due to selection effects. We underscore the significance of long-term ground-based monitoring of hot stars and space-based targeting of hot stars with the Transiting Exoplanet Survey Satellite (TESS) to search for inflated giants in longer-period orbits.