We report the discovery of the first hot Jupiter in the Hyades open cluster. HD 285507b orbits a V = 10.47 K4.5V dwarf (M _* = 0.734 M _☉; R _* = 0.656 R _☉) in a slightly eccentric () orbit with a period of days. The induced stellar radial velocity corresponds to a minimum companion mass of M _Psin i = 0.917 ± 0.033 M _Jup. Line bisector spans and stellar activity measures show no correlation with orbital phase, and the radial velocity amplitude is independent of wavelength, supporting the conclusion that the variations are caused by a planetary companion. Follow-up photometry indicates with high confidence that the planet does not transit. HD 285507b joins a small but growing list of planets in open clusters, and its existence lends support to a planet formation scenario in which a high stellar space density does not inhibit giant planet formation and migration. We calculate the circularization timescale for HD 285507b to be larger than the age of the Hyades, which may indicate that this planet's non-zero eccentricity is the result of migration via interactions with a third body. We also demonstrate a significant difference between the eccentricity distributions of hot Jupiters that have had time to tidally circularize and those that have not, which we interpret as evidence against Type II migration in the final stages of hot Jupiter formation. Finally, the dependence of the circularization timescale on the planetary tidal quality factor, Q _P, allows us to constrain the average value for hot Jupiters to be .