Principle and design of the intense positron source facility at the new Munich research reactor FRM-II is presented. Absorption of high energy prompt gamma rays from thermal neutron capture in (113) Cd generates positrons by pair production. For this purpose, a cadmium cap will be placed inside a beam tube in the neutron field of the reactor, where an undisturbed thermal neutron flux up to 2.10(14) n.cm(-2) s(-1) is expected. At this position the flux ratio of thermal to fast neutron will be better than 10(4). Monte Carlo calculation showed that a mean capture rate in cadmium between 4.5 and 6.0.10(13) n.cm(-2)s(-1) can be expected. Absorption of gamma rays would lead to a heat impact less than 4 Wcm(-2). Inside the cadmium cap a structure of platinum is placed for converting the gamma radiation into positron-electron pairs. As converting material platinum is used, since the cross section for pair production is even higher than in tungsten. The heated platinum foils also act as moderators. The positron beam with a primary energy of about 5 keV is formed by electric lenses and magnetic fields. A remoderation stage leads to an improvement of the positron beam brilliance, where an intensity of about 10(9) slow positrons per second can be expected.