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(circle dot) , R-* = 2.546(-0.084)(+0.099) R-circle dot host star in a similar to 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 vsin I-* = 35.8 +/- 1.1 km s(-1), 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 degrees, 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.