All elementary steps of a chemical reaction have been successfully induced on individual molecules with a scanning tunneling microscope (STM) in a controlled step-by-step manner utilizing a variety of manipulation techniques. The reaction steps involve the separation of iodine from iodobenzene by using tunneling electrons, bringing together two resultant phenyls mechanically by lateral manipulation and, finally, their chemical association to form a biphenyl molecule mediated by excitation with tunneling electrons. The procedures presented here constitute an important step towards the assembly of individual molecules out of simple building blocks in situ on the atomic scale.