Recognition of the potentially massive computational power of a quantum computer has driven a considerable experimental effort to build such a device. Of the various possible physical implementations, silicon-based architectures are attractive for the long spin relaxation times involved, their scalability, and ease of integration with existing silicon technology. However, their fabrication requires construction at the atomic scale-an immense technological challenge. Here we outline a detailed strategy for the construction of a phosphorus in silicon quantum computer and demonstrate the first significant step towards this goal-the fabrication of atomically precise arrays of single phosphorus bearing molecules on a silicon surface. After using a monolayer hydrogen resist to passivate a silicon surface we apply pulsed voltages to a scanning tunnelling microscope tip to selectively desorb individual hydrogen atoms with atomic resolution. Exposure of this surface to the phosphorus precursor phosphine results in precise placement of single phosphorus atoms on the surface. We also describe preliminary studies into a process to incorporate these surface phosphorus atoms into the silicon crystal at the array sites.