It is argued that 79Kr is uniquely suited for an intense positron source. It can be produced by neutron activation of a rare, but available, stable isotope 78Kr; it has a convenient 35-h half-life; as a nonreactive gas, it can be transported and recycled in a closed system using automated valves without exposure of personnel; and it can be vapor deposited easily on a large area cold surface using a solid neon moderator to make a slow positron source with intensity (∼1011 s−1) limited only by the availability of neutrons and cryogenic refrigeration.