We present the Transiting Exoplanet Survey Satellite (TESS) Habitable Zone Stars Catalog, a list of 1822 nearby stars with a TESS magnitude brighter than T = 12 and reliable distances from Gaia DR2, around which the NASAs TESS mission can detect transiting planets, which receive Earth-like irradiation. For all those stars TESS is sensitive down to 2 Earth radii transiting planets during one transit. For 408 stars TESS can detect such planets down to 1 Earth size during one transit. For 1690 stars, TESS has the sensitivity to detect planets down to 1.6 times Earth-size, a commonly used limit for rocky planets in the literature, receiving Earth-analog irradiation. We select stars from the TESS Candidate Target List, based on TESS Input Catalog Version 7. We update their distances using Gaia Data Release 2, and determine whether the stars will be observed for long enough during the 2 year prime mission to probe their Earth equivalent orbital distance for transiting planets. We discuss the subset of 227 stars for which TESS can probe the full extent of the Habitable Zone, the full region around a star out to about a Mars-equivalent orbit. Observing the TESS Habitable Zone Catalog Stars will also give us deeper insight into the occurrence rate of planets, out to Earth-analog irradiation as well as in the Habitable Zone, especially around cool stars. We present the stars by decreasing angular separation of the 1AU equivalent distance to provide insights into which stars to prioritize for ground-based follow-up observations with upcoming extremely large telescopes.
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