  We present results from a 49.3 ks Chandra X-ray observation of the strongly
interacting dumbbell galaxies NGC4782(3C278) and NGC4783 that constrain the
kinematics of the interaction and models for bending the radio jets associated
with NGC4782. The galaxies are embedded in an approximately spherical
distribution of group gas, centered on NGC4782,that is nearly isothermal with
mean kT ~ 1.4+/- 0.4 keV. The X-ray morphology suggests that NGC4783 is
infalling into a single, massive galaxy group (LGG316) with NGC4782 nearly at
rest at the center of the group potential.NGC4783 shows a sharp X-ray surface
brightness edge (cold front) to the east and a ~15 kpc ram-pressure-stripped
tail to the west. Analysis of this cold front indicates NGC4783 is moving east
with a total velocity ~870+270-400 km/s (Mach ~1.4+0.5-0.7) at an inclination
angle ~46 deg.(>33 deg.)towards us with respect to theplane of the sky. A
~45Myr old X-ray cavity, with enthalpy of 4.4 x 10^{57}ergs, coincides with the
eastern radio lobe of 3C278. X-ray knots are found on both the radio jet and
counter-jet, coincident with peaks in the radio emission. Assuming a light,
mildly relativistic jet in 3C278, ram pressure velocities of 100-200 km/s
impacting the eastern jet and ~170 km/s acting on the western radio lobe are
sufficient to produce their observed bending. These velocities may be caused by
bulk motions established in the IGM by the high velocity interaction between
the galaxies, by the motion of NGC4782 relative to the IGM, or both.
