Direct imaging allows for the detection and characterization of exoplanets via their thermal emission. We report the discovery via imaging of a young Jovian planet in a triple-star system and characterize its atmospheric properties through near-infrared spectroscopy. The semimajor axis of the planet is closer relative to that of its hierarchical triple-star system than for any known exoplanet within a stellar binary or triple, making HD 131399 dynamically unlike any other known system. The location of HD 131399Ab on a wide orbit in a triple system demonstrates that massive planets may be found on long and possibly unstable orbits in multistar systems. HD 131399Ab is one of the lowest mass (4 +/- 1 Jupiter masses) and coldest (850 +/- 50 kelvin) exoplanets to have been directly imaged.