Positron emission tomography (PET) relies upon the detection of photons resulting from the annihilation of positrons emitted by a radiopharmaceutical. The combination of images obtained with PET and magnetic resonance imaging (MRI) have begun to greatly enhance the study of many physiological processes. A combined MRI-PET scanner could alleviate much of the spatial and temporal coregistration difficulties currently encountered in utilizing images from these complementary imaging modalities. In addition, the resolution of the PET scanner could be improved by the effects of the magnetic field. In this computer study, the utilization of a strong static homogeneous magnetic field to increase PET resolution by reducing the effects of positron range and photon noncollinearity was investigated. The results reveal that significant enhancement of resolution can be attained. For example, an approximately 27% increase in resolution is predicted for a PET scanner incorporating a 10-Tesla magnetic field. Most of this gain in resolution is due to magnetic confinement of the emitted positrons. Although the magnetic field does mix some positronium states resulting in slightly less photon noncollinearity, this reduction does not significantly affect resolution. Photon noncollinearity remains as the fundamental limiting factor of large PET scanner resolution.