Abell~1142 is a low-mass galaxy cluster at low redshift containing two comparable Brightest Cluster Galaxies (BCG) resembling a scaled-down version of the Coma Cluster. Our Chandra analysis reveals an X-ray emission peak, roughly 100 kpc away from either BCG, which we identify as the cluster center. The emission center manifests itself as a second beta-model surface brightness component distinct from that of the cluster on larger scales. The center is also substantially cooler and more metal rich than the surrounding intracluster medium (ICM), which makes Abell 1142 appear to be a cool core cluster. The redshift distribution of its member galaxies indicates that Abell 1142 may contain two subclusters with each containing one BCG. The BCGs are merging at a relative velocity of ~1200 km/s. This ongoing merger may have shock-heated the ICM from ~ 2 keV to above 3 keV, which would explain the anomalous L_X--T_X scaling relation for this system. This merger may have displaced the metal-enriched cool core of either of the subclusters from the BCG. The southern BCG consists of three individual galaxies residing within a radius of 5 kpc in projection. These galaxies should rapidly sink into the subcluster center due to the dynamical friction of a cuspy cold dark matter halo.