We present a new setup for a symmetric electron-electron scattering experiment to observe spin coincidences of scattered electron pairs. In the presented Moeller scattering experiment the symmetric scattered electrons differ from each other only by their spin direction. At these conditions a spin entanglement of the scattered electrons is expected. To demonstrate this spin entanglement, a single particle resolved spin measurement of the electrons has to be performed. The expected spin asymmetry has been investigated with two Mott polarimeters, where one Mott polarimeter was rotated up to 901 around the beam axis relative to the scattering plane of the second Mott analyzer. We obtainhere a number of measured coincidences using both Mott polarimeters, whicht exceeds the background of random coincidences by a ratio of four or higher. The reduction of the measured spin coincidences with the increasing angle between the scattering planes is in agreement with the quantum mechanical expectations. However, because of the low total efficiency of effi10 Γ 5 for the coincident spin detection further improvements of the setup are intended to minimize the statistical error of the measurement in order to prove the expected electron spin entanglement.