We report the discovery of HAT-P-67b, which is a hot-Saturn transiting a rapidly rotating F-subgiant. HAT-P-67b has a radius of R_p_=2.085_-0.071_^+0.096^ R_J_, and orbites a M_*_=1.642_-0.072_^+0.155^ M_{sun}_, R_*_=2.546_-0.084_^+0.099^ R_{sun}_ host star in a ~4.81 day period orbit. We place an upper limit on the mass of the planet via radial velocity measurements to be M_p_<0.59 M_J_, and a lower limit of >0.056 M_J_ by limitations on Roche lobe overflow. Despite being a subgiant, the host star still exhibits relatively rapid rotation, with a projected rotational velocity of vsini_*_=35.8+/-1.1 km/s, which makes it difficult to precisely determine the mass of the planet using radial velocities. We validated HAT-P-67b via two Doppler tomographic detections of the planetary transit, which eliminate potential eclipsing binary blend scenarios. The Doppler tomographic observations also confirm that HAT-P-67b has an orbit that is aligned to within 12{deg}, in projection, with the spin of its host star. HAT-P-67b receives strong UV irradiation and is among one of the lowest density planets known, which makes it a good candidate for future UV transit observations in the search for an extended hydrogen exosphere.