We report the discovery of KELT-7b, a transiting hot Jupiter with a mass of 1.28+/-0.18M_J_, radius of 1.533^+0.046^_-0.047_R_J_, and an orbital period of 2.7347749+/-0.0000039days. The bright host star (HD33643; KELT-7) is an F-star with V=8.54, T_eff_=6789^+50^_-49_K, [Fe/H]=0.139^+0.075^_-0.081_, and logg=4.149+/-0.019. It has a mass of 1.535^+0.066^_-0.054_M_{Sun}_, a radius of 1.732^+0.043^_-0.045_R_{Sun}_, and is the fifth most massive, fifth hottest, and the ninth brightest star known to host a transiting planet. It is also the brightest star around which Kilodegree Extremely Little Telescope (KELT) has discovered a transiting planet. Thus, KELT-7b is an ideal target for detailed characterization given its relatively low surface gravity, high equilibrium temperature, and bright host star. The rapid rotation of the star (73+/-0.5km/s) results in a Rossiter-McLaughlin effect with an unusually large amplitude of several hundred m/s. We find that the orbit normal of the planet is likely to be well-aligned with the stellar spin axis, with a projected spin-orbit alignment of {lambda}=9.7{deg}+/-5.2{deg}. This is currently the second most rapidly rotating star to have a reflex signal (and thus mass determination) due to a planetary companion measured.