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 $T_{rm eff}$ =$5645pm50$ K, a mass of $M_{star}$ = $1.128^{+0.065}_{-0.061}$ $M_{odot}$, radius of $R_{star}$ = $1.777^{+0.047}_{-0.044}$ $R_{odot}$, a surface gravity of $log$ $g_{star}$ = $3.993^{+0.027}_{-0.028}$, and an age of $7.4^{+1.6}_{-1.5}$ Gyr. Its planetary companion (TOI-172 b) has a radius of $R_{rm P}$ = $0.965^{+0.032}_{-0.029}$ $R_{rm J}$, a mass of $M_{rm P}$ = $5.42^{+0.22}_{-0.20}$ $M_{rm J}$, and is on an eccentric orbit ($e = 0.3806^{+0.0093}_{-0.0090}$). 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.
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