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 T _ { eff } = 6278 \pm 51 K , \log { g _ { \star } } = 3.89 ^ { +0.054 } _ { -0.051 } , and [ Fe/H ] = 0.19 ^ { +0.083 } _ { -0.085 } , with an inferred mass { M } _ { * } = 1.59 ^ { +0.071 } _ { -0.091 } { M } _ { \Sun } and radius { R } _ { * } = 2.37 \pm 0.18 { R } _ { \Sun } . The planetary companion has { M } _ { P } = 0.95 \pm 0.14 { M } _ { J } , { R } _ { P } = 1.79 ^ { +0.18 } _ { -0.17 } { R } _ { J } , \log { g _ { P } } = 2.87 ^ { +0.097 } _ { -0.098 } , and density \rho _ { P } = 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 { BJD _ { TDB } } is 2457088.692055 \pm 0.0009 and the period is P = 5.0316144 \pm 0.0000306 days . Despite the relatively large separation of \sim 0.07 AU implied by its \sim 5.03 -day orbital period , KELT-12b receives significant flux of 2.93 ^ { +0.33 } _ { -0.30 } \times 10 ^ { 9 } erg s ^ { -1 } cm ^ { -2 } from its host . We compare the radii and insolations of transiting gas-giant planets around hot ( T _ { eff } \geq 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 gas giants in longer-period orbits .