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^(+0.096)_(-0.071) R_J, and orbites a M* = 1.642^(+0.155)_(-0.072) M⊙, R* = 2.546^(+0.099)_(-0.084) R⊙ 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 0.056 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 ν sin 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°, 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
