The feasibility of using a radio-frequency quadrupole (RFQ) accelerator to accelerate 3He++for use in positron emission tomography (PET) is shown. The 3He++ RFQ is extremely lightweight in comparison to a cyclotron, but can nevertheless produce all four radioisotopes of interest (18F, 13N, 15O, and 11C) in more than adequate quantities. Due to the neutron-poor nature of 3He++, the desired positron emitters can be produced from naturally abundant target isotopes. In addition, target reactions and collisions with the accelerating structure produce relatively small numbers of neutrons compared to proton and deuteron systems. This yields two economic advantages. Enriched 13C, 15N, and 18O target materials are not required. Also, the shielding requirements are reduced considerably, and there is no need for radiation shielding around the accelerator. This reduced shielding results in a factor of 8 reduction in total facility shielding weight compared to a proton/deuteron cyclotron facility. The order of magnitude reduction in facility weight, the virtual elimination of the accelerator weight, and the relative lack of residual induced activity gives rise to the possibility of a radiopharmaceutical production system that is less expensive than present systems and may ultimately be transportable. Such a system could make PET imaging technology far more accessible geographically and financially than it is at present.