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Silicon drift detectors (SDD) with on-chip electronics have found many applications in different fields. A detector system has recently been designed and built to study the electrons from Compton scatter events in such a detector. The reconstruction of the Compton electrons is a crucial issue for Compton imaging. The equipment consists of a monolithic array of 19 channel SDDs and an Anger camera. Photons emitted from a finely-collimated source undergo Compton scattering within the SDD where the recoil electron is absorbed. The scattered photon is subsequently observed by photoelectric absorption in the second detector. The coincidence events are used to get the energy, position, and direction of the Compton electrons. Because the on-chip transistors provide the first stage amplification, the SDDs provide outstanding noise performance and fast shaping, so that very good energy resolution can be obtained even at room temperature. The drift detectors require a relatively low number of readout channels for large detector areas. Custom-designed analog and digital electronics provide fast readout of the SDDs. The equipment is designed such that the measurements can be done in all detector orientations and kinematical conditions. The first results obtained with this detector system will be presented in this paper.