We report the discovery of TrES-4, a hot Jupiter that transits the star GSC 02620-00648 every 3.55 days. From high-resolution spectroscopy of the star, we estimate a stellar effective temperature of Teff=6100+/-150 K, and from high-precision z and B photometry of the transit we constrain the ratio of the semimajor axis a and the stellar radius R* to be a/R*=6.03+/-0.13. We compare these values to model stellar isochrones to constrain the stellar mass to be M*=1.22+/-0.17 Msolar. Based on this estimate and the photometric time series, we constrain the stellar radius to be R*=1.738+/-0.092 Rsolar and the planet radius to be Rp=1.674+/-0.094 RJup. We model our radial velocity data assuming a circular orbit and find a planetary mass of 0.84+/-0.10 MJup. Our radial velocity observations rule out line-bisector variations that would indicate a specious detection resulting from a blend of an eclipsing binary system. TrES-4 has the largest radius and lowest density of any of the known transiting planets. It presents a challenge to current models of the physical structure of hot Jupiters and indicates that the diversity of physical properties among the members of this class of exoplanets has yet to be fully explored.