Proton therapy is a treatment modality of increasing utility in clinical radiation oncology mostly because its dose distribution conforms more tightly to the target volume than x-ray radiation therapy. One important feature of proton therapy is that it produces a small amount of positron-emitting isotopes along the beam-path through the non-elastic nuclear interaction of protons with target nuclei. These radioisotopes allow imaging the therapy dose distribution using positron emission tomography (PET). The resulting PET images provide a powerful tool for quality assurance of the treatment, especially when treating inhomogeneous organs such as the lungs or the head-and-neck, where the calculation of the dose distribution for treatment planning is more difficult. This paper uses Monte Carlo simulations to predict the yield of positron emitters produced by a 250 MeV proton beam, and to simulate the productions of the image in a clinical PET scanner.