We report the discovery of KELT-3b, a moderately inflated transiting hot Jupiter with a mass of 1.477 (-0.067, +0.066) M_J, and radius of 1.345 +/- 0.072 R_J, with an orbital period of 2.7033904 +/- 0.000010 days. The host star, KELT-3, is a V=9.8 late F star with M_* = 1.278 (-0.061, +0.063) M_sun, R_* = 1.472 (-0.067, +0.065) R_sun, T_eff = 6306 (-49, +50) K, log(g) = 4.209 (-0.031, +0.033), and [Fe/H] = 0.044 (-0.082, +0.080), and has a likely proper motion companion. KELT-3b is the third transiting exoplanet discovered by the KELT survey, and is orbiting one of the 20 brightest known transiting planet host stars, making it a promising candidate for detailed characterization studies. Although we infer that KELT-3 is significantly evolved, a preliminary analysis of the stellar and orbital evolution of the system suggests that the planet has likely always received a level of incident flux above the empirically-identified threshold for radius inflation suggested by Demory & Seager (2011).