A measurement of beam helicity asymmetries in the reaction 3He(e,en)pp has been performed at the Mainz Microtron in quasielastic kinematics in order 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 were scattered on a highly polarized 3He gas target. The scattered electrons were detected with a high-resolution magnetic spectrometer, and the ejected neutrons with a dedicated neutron detector composed of scintillator bars. To reduce systematic errors data were taken for four different target polarization orientations allowing the determination of GEn/GMn from a double ratio. We find mu_n GEn/GMn = 0.250 +/- 0.058(stat.) +/- 0.017 (sys.).