  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 $T_{\rm eff}$ =$5645\pm50$ 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.
