A detector has been developed for position sensitive registration of annihilation radiation. The 511 keV gamma rays are detected in a set of BaF2 scintillation crystals coupled to low pressure TMAE-filled photosensitive multi wire chambers. In a first experimental detector with two BaF2 crystals we obtained a detection efficiency for 511 keV quanta of 42%. The position resolution is 5 mm and the time resolution is 4 ns. At present a circular detector for three BaF2 crystals with a diameter of 28 cm, each with a thickness of 8 mm, is under construction. Position sensitivity is obtained by means of delayline read out of cathode wires. Detectors of this type can be used as building blocks for a PET system. We are performing simulations of a system consisting of six rectangular detectors in a hexagonal composition. Results are given and a discussion of further innovative developments is presented.