With the Chandra X-ray Telescope we have detected a zero-redshift OVII He-alpha absorption line along the sight line toward 3C 273. This line detection is highly significant, with a signal-to-noise ratio (S/N) of 6.4. We explore two models, which associate this line with (1) the intragroup gas in the Local Group, and (2) the hot halo gas in the vicinity of our Milky Way. In the first model, we find that for a standard beta-model of the gas distribution in the Local Group, the temperature is constrained to 2.3e5 < T < 1.2e6 K and the baryon overdensity is delta_b ~ 100; both results are consistent with the properties of the so-called warm-hot intergalactic medium (WHIM) predicted by cosmological simulations. We also find the core radius of the gas distribution should be > 100 kpc. In the second model we discuss several possible Galactic origins for the absorption, and we comment on the possibility that the OVII is associated with the OVI absorption observed in this direction by the Far Ultraviolet Spectroscopic Explorer (FUSE). We find that there is a strong indication that collisional ionization is the dominant ionization source for the observed absorption.