We report the discovery of TOI-2180b, a 2.8M_J_ giant planet orbiting a slightly evolved G5 host star. This planet transited only once in Cycle 2 of the primary Transiting Exoplanet Survey Satellite (TESS) mission. Citizen scientists identified the 24hr single-transit event shortly after the data were released, allowing a Doppler monitoring campaign with the Automated Planet Finder telescope at Lick Observatory to begin promptly. The radial velocity observations refined the orbital period of TOI-2180b to be 260.8{+/-}0.6days, revealed an orbital eccentricity of 0.368{+/-}0.007, and discovered long-term acceleration from a more distant massive companion. We conducted ground-based photometry from 14 sites spread around the globe in an attempt to detect another transit. Although we did not make a clear transit detection, the nondetections improved the precision of the orbital period. We predict that TESS will likely detect another transit of TOI-2180b in Sector 48 of its extended mission. We use giant planet structure models to retrieve the bulk heavy-element content of TOI-2180b. When considered alongside other giant planets with orbital periods over 100days, we find tentative evidence that the correlation between planet mass and metal enrichment relative to stellar is dependent on orbital properties. Single-transit discoveries like TOI-2180b highlight the exciting potential of the TESS mission to find planets with long orbital periods and low irradiation fluxes despite the selection biases associated with the transit method.