We present a new Chandra X-ray observation of the off-axis galaxy group merger RXJ0751.3+5012. The hot atmospheres of the two colliding groups appear highly distorted by the merger. The images reveal arc-like cold fronts around each group core, produced by the motion through the ambient medium, and the first detection of a group merger shock front. We detect a clear density and temperature jump associated with a bow shock of Mach number M=1.9+/-0.4 ahead of the northern group. Using galaxy redshifts and the shock velocity of 1100+/-300 km/s, we estimate that the merger axis is only 10deg from the plane of the sky. From the projected group separation of 90 kpc, this corresponds to a time since closest approach of 0.1 Gyr. The northern group hosts a dense, cool core with a ram pressure stripped tail of gas extending 100 kpc. The sheared sides of this tail appear distorted and broadened by Kelvin-Helmholtz instabilities. We use the presence of this substructure to place an upper limit on the magnetic field strength and, for Spitzer-like viscosity, show that the development of these structures is consistent with the critical perturbation length above which instabilities can grow in the intragroup medium. The northern group core also hosts a galaxy pair, UGC4052, with a surrounding IR and near-UV ring 40 kpc in diameter. The ring may have been produced by tidal stripping of a smaller galaxy by UGC4052 or it may be a collisional ring generated by a close encounter between the two large galaxies.