  We search for highly-ionized gas near three AGN host galaxies using the
Chandra low-energy transmission grating spectrograph. Strong absorption lines
from such gas are seen at z=0, most likely from one or more of the following
components: (1) a Galactic corona, (2) the Local Group medium, and (3) an
extended warm-hot intergalactic medium (WHIM) filament passing through our
local overdensity. Since AGNs reside within host galaxies that are also
expected to sit within cosmically overdense regions, similar absorption
resulting from these three components should appear at the AGN redshifts as
well. However, no such absorption is seen. The lack of strong absorption lines
is likely a result of the gas in these host galaxies and surrounding galaxy
clusters being much hotter, and hence more highly ionized, than the gas in the
Local Group+Galaxy system. We conclude that WHIM filaments produce no
measurable absorption lines at the AGN redshifts, and therefore contribute at
most a small fraction of the observed z=0 warm-hot gas.
