  We present an X-ray analysis of 54 normal elliptical galaxies in the Chandra
archive and isolate their hot gas component from the contaminating point source
emission, allowing us to conduct, for the first time, a morphological analysis
on the gas alone. A comparison with optical images and photometry shows that
the hot gas morphology has surprisingly little in common with the shape of the
stellar distribution. We observe no correlation between optical and X-ray
ellipticities in the inner regions where stellar mass dominates over dark
matter. A shallow correlation would be expected if the gas had settled into
hydrostatic equilibrium with the gravitational potential. Instead, observed
X-ray ellipticities exceed optical ellipticities in many cases. We exclude
rotation as the dominant factor to produce the gas ellipticities. The gas
appears disturbed, and hydrostatic equilibrium is the exception rather than the
rule. Nearly all hydrostatic models can be ruled out at 99% confidence, based
of their inability to reproduce the optical-X-ray correlation and large X-ray
ellipticities. Hydrostatic models not excluded are those in which dark matter
either dominates over stellar mass inside the inner half-light radius or has a
prominently cigar-shaped distribution, both of which can be ruled out on other
grounds. We conclude that, even for rather X-ray faint elliptical galaxies, the
gas is at least so far out of equilibrium that it does not retain any
information about the shape of the potential, and that X-ray derived radial
mass profiles may be in error by factors of order unity.
