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 > 3 \sigma . 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 . In the southern Galactic hemisphere , we identify absorption along the sight line to Fairall 9 with the Magellanic Stream and this gas has 10 ^ { 5.75 } < T < 10 ^ { 6.35 } K if CIE applies . There may be a blend of O vii absorption features along the sight line towards Mkn 509 . LG clouds along this sight line may interact with a hot Galactic corona or a low density LG medium . The sight line to 3C 120 does not appear to be associated either with local structure or UV absorbing gas , and may correspond to the local hot IGM . Gas in the Magellanic Stream extension along the sight line to Akn 564 has T < 10 ^ { 6.1 } K if it is in CIE. 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 .