We present Chandra X-ray observations of galaxy cluster A168 (z=0.045). Two X-ray peaks with a projected distance of 676 kpc are found to be located close to two dominant galaxies, respectively. Both peaks are significantly offset from the peak of the number density distribution of galaxies. This suggests that A168 consists of two subclusters, a northern subcluster (A168N) and a southern subcluster (A168S). Further X-ray imaging analysis reveals that (1) the X-ray isophotes surrounding the two X-ray peaks are heavily distorted and (2) an elongated and continuous filament connects the two X-ray peaks. These suggest that strong interactions have occurred between the two subclusters. Spectral analysis shows that A168 has a mean temperature of 2.53+/-0.09 keV and a mean metallicity of 0.31+/-0.04 Z(circle dot). The metallicity is roughly a constant across the cluster, but the temperature shows some systematic variations. Most X-ray, optical, and radio properties of A168 are consistent with it being an off-axis merger several gigayears after a core passage, although detailed numerical simulations are required to see whether the observed properties, in particular the significant offset between the optical and X-ray centers, can be reproduced in such a scenario.