We report the first localization of diffuse, non-thermal, X-ray emission from a nearby galaxy cluster. Using Chandra data, we have isolated a diffuse non-thermal X-ray component with a photon index, Gamma_ X = 2.21 +0.14 -0.15 and a flux of 9.5 +1.1 -2.5 x 10^-5 photons cm^-2 s^-1 keV^-1 at 1 keV, that extends from ~1.5 to ~2.5 to the south of the X-ray flux peak. Comparison to simulations implies that the diffuse non-thermal emission is produced by primary electrons, accelerated at shocks to relativistic velocities. Using these results and the flux and hardness maps produced with data from the Chandra Advanced CCD Imaging Spectrometer, we conclude that a smaller subclump coming from the north merged with IC1262. The offset of the cD galaxy from the X-ray peak and large peculiar velocity indicate that the subclumps impact parameter was to the west and on the near side of IC1262.