  The Transiting Exoplanet Survey Satellite TESS has begun a new age of
exoplanet discoveries around bright host stars. We present the discovery of HD
1397b (TOI-120.01), a giant planet in an 11.54day eccentric orbit around a
bright (V=7.9) G-type subgiant. We estimate both host star and planetary
parameters consistently using EXOFASTv2 based on TESS time-series photometry of
transits and CORALIE radial velocity measurements. We find that HD 1397b is a
Jovian planet, with a mass of $0.419\pm-0.024$ M$_{\rm Jup}$ and a radius of
$1.023^{+0.023}_{-0.026$}$ R$_{\rm Jup}$. Characterising giant planets in
short-period eccentric orbits, such as HD 1397b, is important for understanding
and testing theories for the formation and migration of giant planets as well
as planet-star interactions.
