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 $0.419pm-0.024$ 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.
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