  We present results from a 25 ksec CHANDRA ACIS-S observation of galaxies
NGC4438 and NGC4435 in the Virgo Cluster. X-ray emission in NGC4438 is observed
in a ~700 pc nuclear region, a 2.3 kpc spherical bulge, and a network of
filaments extending 4-10 kpc to the W and SW of the galaxy. The X-ray emission
in all 3 regions is highly correlated to similar features observed in Halpha.
Spectra of the filaments and bulge are well represented by a 0.4 keV MEKAL
model with combined 0.3-2 keV intrinsic luminosity of 1.24x10^{40}erg/s,
electron densities ~ 0.02-0.04 cm^{-3}, cooling times of 400-700 Myr and X-ray
gas mass <~ 3.7x10^8 Msolar. In the nuclear region of NGC4438 X-ray emission is
seen from the nucleus and from two outflow bubbles extending 360(730) pc to the
NW(SE) of the nucleus. The spectrum of the NW outflow bubble plus nucleus is
well fitted by an absorbed (n_H=1.9x10^{21} cm^{-2}) 0.58 keV MEKAL plasma
model plus a heavily absorbed (n_H = 2.9 x10^{22} cm^{-2}) Gamma = 2, power law
component. The electron density, cooling time, and X-ray gas mass in the NW
outflow are ~0.5 cm^{-3}, 30 Myr and 3.5x10^6 Msolar. Weak X-ray emission is
observed in the central region of NGC4435 with the peak of the hard emission
coincident with the galaxy's optical center; while the peak of the soft X-ray
emission is displaced 316 pc to the NE. The spectrum of NGC 4435 is well fitted
by a non-thermal power law plus a thermal component from 0.2-0.3 keV diffuse
ISM gas. We argue that the X-ray properties of gas outside the nuclear region
in NGC4438 and in NGC4435 favor a high velocity, off-center collision between
these galaxies ~ 100 Myr ago; while the nuclear X-ray emitting outflow gas in
NGC4438 has been heated only recently (within ~ 1-2 Myr) by shocks (v_s ~ 600
kms^{-1}) possibly powered by a central AGN.
