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We report the discovery of a faint (L_x ~ 4 10^37 erg/s, 0.5-2 keV), out-flowing gaseous hot interstellar medium (ISM) in NGC 3379. This represents the lowest X-ray luminosity ever measured from a hot phase of the ISM in a nearby early type galaxy. The discovery of the hot ISM in a very deep Chandra observation was possible thanks to its unique spectral and spatial signatures, which distinguish it from the integrated stellar X-ray emission, responsible for most of the unresolved emission in the Chandra data. This hot component is found in a region of about 800 pc in radius at the center of the galaxy and has a total mass M~ 3 10^5 solar masses. Independent theoretical prediction of the characteristics of an ISM in this galaxy, based on the intrinsic properti es of NGC 3379, reproduce well the observed luminosity, temperature, and radial distribution and mass of the hot gas, and indicate that the gas is in an outflowing phase, predicted by models but not observed in any system so far.