Studies of tearing instabilities and magnetic reconnection in the terrestrial magnetotail must consider the effect of the finite normal field component Bz. Three-dimensional (3-D) particle-in-cell simulations with an open geometry are used to investigate the impact of an externally applied convection electric field on the stability of a moderately thick (1.6c/ωpi) current sheet configuration containing a nonzero Bz. The driving field is localized in the direction of the main magnetic field (x) but is uniform in the cross-tail (y) direction. The initial response of the current sheet to the driving field is dominated by the formation of an embedded electron current layer on the scale of the electron inertial length. This layer forms nearly uniformly in y; cross-tail modes do not play an important role. Once the normal field is driven southward in a local region of the sheet, global scale reconnection is initiated at a rate comparable to that seen in studies of simple 1-D current sheets. The formation of the thin electron current layer is accompanied by the development of an electrostatic potential structure which serves to confine the ions in the thin electron layer and to deflect the ions into the outflow region. The reconnection process forms a high-energy tail on the electron distribution extending up to ~mec2. These high-energy electrons are accelerated in the thin electron current sheet and then spread out along the separatrices.