We describe the discovery of a massive transiting hot Jupiter with a very short orbital period (1.30619 days), which we name TrES-3. From spectroscopy of the host star GSC 03089-00929, we measure Teff=5720+/-150 K, logg=4.6+/-0.3, and vsini<2 km s-1 and derive a stellar mass of 0.90+/-0.15 Msolar. We estimate a planetary mass of 1.92+/-0.23 MJup, based on the sinusoidal variation of our high-precision radial velocity measurements. This variation has a period and phase consistent with our transit photometry. Our spectra show no evidence of line bisector variations that would indicate a blended eclipsing binary star. From detailed modeling of our B and z photometry of the 2.5% deep transits, we determine a stellar radius 0.802+/-0.046 Rsolar and a planetary radius 1.295+/-0.081 RJup. TrES-3 has one of the shortest orbital periods of the known transiting exoplanets, facilitating studies of orbital decay and mass loss due to evaporation, and making it an excellent target for future studies of infrared emission and reflected starlight. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among Caltech, the University of California, and NASA. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.