The deployment of a long tether to operate as a partial space elevator, starting from a nucleus in geostationary orbit, is studied. Uncontrolled deployment is an inherently unstable process because the center of orbit gradually decreases from the geostationary altitude when deployment progresses. It is also observed that the elasticity of the tether has an important effect on deployment stability. It is shown that the application of a transverse force on the main spacecraft, determined by using linear state feedback and appropriate gains, can stabilize the deployment. An LQR controller is developed. Simulations of the dynamics of the system are carried out using this controller for various parametric values of tether elasticity, deployment rates, etc., to evaluate the efficacy of the controller.