Exoplanet characterization typically begins with a measurement of planet mass and radius. The standard method of measuring a planet’s radius requires the planet to transit, which severely biases the sample to those with orbital periods of a few dozen days or less. The resulting dearth of well characterized exoplanets at wider separations hinders our ability to answer fundamental questions of planetary formation, evolution, and even habitability. Here, we introduce the Giant Outer Transiting Exoplanet Mass (GOT 'EM) Survey, an ongoing long-term campaign at the Keck I telescope to measure the masses of giant transiting planets with orbital periods of hundreds to 1,000 days. The GOT 'EM survey is substantially increasing the number of weakly irradiated giant planets with measured mass and radius. This effort is complementary to the characterization of short-period exoplanets and enables novel comparisons between exoplanets and the Solar System giants. The first result of this survey is the confirmation of a 5 Jupiter-mass giant planet in the Kepler-1514 system with an eccentric (e=0.4), 217-day orbit. Known as Kepler-1514b, this planet is one of only a rare few giant planets that receives low enough stellar irradiation that its size, and thereby density, are not affected by radius inflation. We also validate the existence of Kepler-1514c, a transiting Earth-size planet with an orbital period of 10.5 days previously known only as a Kepler Object of Interest. Given the brightness of the host star (V=11.8), we explore this system’s potential for continued follow-up characterization, including a possible measurement of stellar obliquity. Finally, we explain how Kepler-1514b, and all of the transiting cool giant planets in the ongoing GOT 'EM survey, are improbable discoveries that greatly inform models of planetary interiors and formation at orbital periods approaching those of the Solar System giant planets.