We use Chandra data to map the gas temperature in the central region of the merging cluster A2142. The cluster is markedly nonisothermal; it appears that the central cooling flow has been disturbed but not destroyed by a merger. The X-ray image exhibits two sharp, bow-shaped, shocklike surface brightness edges or gas density discontinuities. However, temperature and pressure profiles across these edges indicate that these are not shock fronts. The pressure is reasonably continuous across these edges, while the entropy jumps in the opposite sense to that in a shock (i.e., the denser side of the edge has lower temperature, and hence lower entropy). Most plausibly, these edges delineate the dense subcluster cores that have survived a merger and ram pressure stripping by the surrounding shock-heated gas.