We use deep Chandra observations to measure the emissivity of the unresolved X-ray emission in the elliptical galaxy NGC 3379. After elimination of bright, low-mass X-ray binaries with luminosities >10^{36 erg/sec, we find that the remaining unresolved X-ray emission is characterized by an emissivity per unit stellar mass L_x/M_stars ~8.2x10^{27} erg/s/M_sun in the 0.5-2 keV energy band. This value is in good agreement with those previousely determined for the dwarf elliptical galaxy M32, the bulge of the spiral galaxy M31 and the Milky Way, as well as with the integrated X-ray emissivity of cataclysmic variables and coronally active binaries in the Solar neighborhood. This strongly suggests that i) the bulk of the unresolved X-ray emission in NGC 3379 is produced by its old stellar population and ii) the old stellar populations in all galaxies can be characterized by a universal value of X-ray emissivity per unit stellar mass or per unit K band luminosity.