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We report the discovery of an eccentric hot Neptune and a non-transitingouter planet around TOI-1272. We identified the eccentricity of the innerplanet, with an orbital period of 3.3 d and $R_{\rm p,b} = 4.1 \pm 0.2$$R_\oplus$, based on a mismatch between the observed transit duration and theexpected duration for a circular orbit. Using ground-based radial velocitymeasurements from the HIRES instrument at the Keck Observatory, we measured themass of TOI-1272b to be $M_{\rm p,b} = 25 \pm 2$ $M_\oplus$. We also confirmeda high eccentricity of $e_b = 0.34 \pm 0.06$, placing TOI-1272b among the mosteccentric well-characterized sub-Jovians. We used these RV measurements to alsoidentify a non-transiting outer companion on an 8.7-d orbit with a similar massof $M_{\rm p,c}$ sin$i= 27 \pm 3$ $M_\oplus$ and $e_c \lesssim 0.35$.Dynamically stable planet-planet interactions have likely allowed TOI-1272b toavoid tidal eccentricity decay despite the short circularization timescaleexpected for a close-in eccentric Neptune. TOI-1272b also maintains an envelopemass fraction of $f_{\rm env} \approx 11\%$ despite its high equilibriumtemperature, implying that it may currently be undergoing photoevaporation.This planet joins a small population of short-period Neptune-like planetswithin the "Hot Neptune Desert" with a poorly understood formation pathway.

The TESS-Keck Survey. XIII. An Eccentric Hot Neptune with a Similar-Mass Outer Companion around TOI-1272