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Based on two decades of radial velocity (RV) observations using Keck/High Resolution Echelle Spectrometer (HIRES) and McDonald/Tull, and more recent observations using the Automated Planet Finder, we found that the nearby star HR 5183 (HD 120066) hosts a 3 minimum mass planet with an orbital period of yr. The orbit is highly eccentric (e ≃ 0.84), shuttling the planet from within the orbit of Jupiter to beyond the orbit of Neptune. Our careful survey design enabled high cadence observations before, during, and after the planet's periastron passage, yielding precise orbital parameter constraints. We searched for stellar or planetary companions that could have excited the planet's eccentricity, but found no candidates, potentially implying that the perturber was ejected from the system. We did identify a bound stellar companion more than 15,000 au from the primary, but reasoned that it is currently too widely separated to have an appreciable effect on HR 5183 b. Because HR 5183 b's wide orbit takes it more than 30 au (1'') from its star, we also explored the potential of complimentary studies with direct imaging or stellar astrometry. We found that a Gaia detection is very likely, and that imaging at 10 μm is a promising avenue. This discovery highlights the value of long-baseline RV surveys for discovering and characterizing long-period, eccentric Jovian planets. This population may offer important insights into the dynamical evolution of planetary systems containing multiple massive planets.