  (abridged) We searched for evidence of soft X-ray absorption by hot gas in
the vicinity of the Galaxy in a small sample of fifteen type I AGN observed
with the high resolution X-ray gratings on board Chandra. We find that around
half of the sight lines in our sample exhibit absorption due to local H- or
He-like Oxygen (or both) at confidence levels ranging from >90% to >3sigma.
Depending on the sight line, the absorption can be identified with hot gas in
particular local structures, the Local Group (LG) or the putative local hot
intergalactic medium (IGM). Several sight lines in our sample coincide with
sight lines in a study of O VI absorption by local gas, so an assumption of
collisional ionization equilibrium (CIE) allows us to constrain the temperature
of the local hot gas. We show that some portion of the hot absorbing outflows
apparently detected in the spectra of NGC 4051, PDS 456 and PG 1211+143
respectively could actually correspond to absorption by hot local gas since the
outflow velocity from each of these AGN coincides with the respective
cosmological recession velocity of the AGN.
