Epitaxial lead titanate films have been grown on (001) SrTiO3 substrates by reactive molecular beam epitaxy (MBE). Growth of stoichiometric phase-pure epitaxial PbTiO3 films is achieved by supplying a continuous excess of lead and ozone to the surface of the depositing film. Results obtained from RES composition analysis, measured film thicknesses and flux measurements using atomic absorption spectroscopy (AA) indicate that the film growth rate is completely determined by the incident titanium flux supplied to the surface. Atomic force microscopy (AFM) results show that films grow smoothly in a layer-by-layer fashion with an RMS roughness of < 0.5 nm. The sticking coefficient of titanium is determined to be approximately unity while the excess lead, lead oxide and ozone desorb. Lead and ozone beam equivalent pressures have been measured in the MBE environment. Thermodynamic analysis is used to help describe the processes that prevent the incorporation of PbO into films under adsorption-controlled growth conditions.