We report the discovery of TOI-172 b from the Transiting Exoplanet Survey Satellite (TESS) mission, a massive hot Jupiter transiting a slightly evolved G star with a 9.48-day orbital period. This is the first planet to be confirmed from analysis of only the TESS full frame images, because the host star was not chosen as a two-minute cadence target. From a global analysis of the TESS photometry and follow-up observations carried out by the TESS Follow-up Observing Program Working Group, TOI-172 (TIC 29857954) is a slightly evolved star with an effective temperature of T_(eff) = 5645 ± 50 K, a mass of M⋆ = 1.128^(+0.065)_(−0.061) M⊙, radius of R⋆ = 1.777^(+0.047)_(−0.044) R⊙, a surface gravity of log g⋆ = 3.993^(+0.027)_(−0.028), and an age of 7.4^(+1.6)_(−1.5) Gyr. Its planetary companion (TOI-172 b) has a radius of R_P = 0.965^(+0.032)_(−0.029) R_J, a mass of M_P = 5.42^(+0.22)_(−0.20) M_J, and is on an eccentric orbit (e=0.3806^(+0.0093)_(−0.009)). TOI-172 b is one of the few known massive giant planets on a highly eccentric short-period orbit. Future study of the atmosphere of this planet and its system architecture offer opportunities to understand the formation and evolution of similar systems
