Orbital properties of hot Jupiters depend on the temperature and rotation rate of their host stars. These observed correlations provide some of the very few constraints on their dynamical evolution. However, almost all the objects available to such studies orbit around relatively slow rotators, with stellar rotation periods usually several times larger than the orbital periods. Because of the apparent dearth of hot Jupiters around fast rotators, the dynamical evolution of these systems is largely unconstrained. Here, we report the discovery of XO-6b, a hot Jupiter orbiting a fast rotating and bright F5 star (Teff = 6605 K, Vsini = 45 km/s, V = 10.25). This transiting hot Jupiter system is one of the very few with a stellar rotation period smaller than the planet orbital period (Prot < 1.41 d, Porb = 3.77 d), and adds to the sample of hot Jupiters around hot stars with a measured obliquity. We present the system parameters extracted from photometric follow-up and Rossiter-McLaughlin measurements. This system provides an additional constraint to dynamical and tidal models in their promising attempt of explaining the dynamical evolution of close-in giant planets, and will allow to extend the emerging picture to planets orbiting fast rotating stars.