A measurement of beam helicity asymmetries in the reaction 3He[over →](e[over →],e'n)pp is performed at the Mainz Microtron in quasielastic kinematics to determine the electric to magnetic form factor ratio of the neutron GEn/GMn at a four-momentum transfer Q2=1.58 GeV2. Longitudinally polarized electrons are scattered on a highly polarized 3He gas target. The scattered electrons are detected with a high-resolution magnetic spectrometer, and the ejected neutrons are detected with a dedicated neutron detector composed of scintillator bars. To reduce systematic errors, data are taken for four different target polarization orientations allowing the determination of GEn/GMn from a double ratio. We find μnGEn/GMn=0.250±0.058(stat)±0.017(syst).