A beam of slow positrons is required as a tool for a new plasma diagnostic technique. Other applications in particle physics and analytical chemistry exist; e.g., cross-section measurements, analysis of trace elements, etc. Design and construction of a positron gun capable of generating a beam of slow positrons is described. Both 22Na or 58Co are possible positron sources. Employing a 22Na source of 2 mCi, the device produces 1850 slow positrons per second, at a beam radius of 1.9 mm.