The self-assembly mechanism of alkanethiol monolayers on the (111) surface of gold was discovered with the use of an ultrahigh-vacuum scanning tunneling microscope. Monolayer formation follows a two-step process that begins with condensation of low-density crystalline islands, characterized by surface-aligned molecular axes, from a lower density lattice-gas phase. At saturation coverage of this phase, the monolayer undergoes a phase transition to a denser phase by realignment of the molecular axes with the surface normal. These studies reveal the important role of molecule-substrate and molecule-molecule interactions in the self-assembly of these technologically important material systems.