High-eccentricity tidal migration is a possible way for giant planets to be placed in short-period orbits. If this happens often, one would expect to catch proto hot Jupiters on highly elliptical orbits undergoing high-eccentricity tidal migration. As of yet, few such systems have been discovered. Here, we introduce TOI-3362b (TIC-464300749b), an 18.1 day, 5 M Jup planet orbiting a main-sequence F-type star that is likely undergoing higheccentricity tidal migration. The orbital eccentricity is 0.815 -+ 0.032 0.023 . With a semimajor axis of 0.153 -+ 0.003 0.002 au, the planet's orbit is expected to shrink to a final orbital radius of 0.051 -+ 0.006 0.008 au after complete tidal circularization. Several mechanisms could explain the extreme value of the planet's eccentricity, such as planet-planet scattering and secular interactions. Such hypotheses can be tested with follow-up observations of the system, e.g., measuring the stellar obliquity and searching for companions in the system with precise, long-term radial-velocity observations. The variation in the planet's equilibrium temperature as it orbits the host star and the tidal heating at periapse make this planet an intriguing target for atmospheric modeling and observation. Because the planet's orbital period of 18.1 days is near the limit of TESS's period sensitivity, even a few such discoveries suggest that proto hot Jupiters may be quite common.