With an aim to understanding the fundamental mechanisms underlying chemical mechanical planarization ~CMP! of copper, we simulate the nanoscale polishing of a copper surface with molecular dynamics utilizing the embedded atom method. Mechanical abrasion produces rough planarized surfaces with a large chip in front of the abrasive particle, and dislocations in the bulk of the crystal. The addition of chemical dissolution leads to very smooth planarized copper surfaces and considerably smaller frictional forces that prevent the formation of bulk dislocations. This is a first step towards understanding the interplay between mechanistic material abrasion and chemical dissolution in chemical mechanical planarization of copper interconnects.