We have studied the formation of octadecyltrichlorosilane (OTS) monolayers on Si(111) surfaces, using X-ray reflectivity at the solution-substrate interface. We find that the thickness of the OTS layer remains at similar to 25 Angstrom throughout the entire growth process. The electron density of the deposited layer increases monotonically, from very close to that of the solution to that of a densely packed OTS monolayer. We do not observe any increased roughness at the OTS-solution interface of a partially deposited monolayer. This means that the molecules are vertical when deposited and that the films undergo "island-type" growth.