We describe an approach to stabilize a bistable biological system near its unstable equilibrium using a molecular feedback controller. As a case study we focus on the classical toggle switch by Gardner and Collins. The controller relies on two parallel sequestration motifs, which yield two control species influencing the production rates of the toggle switch proteins. We show that the controller reshapes the equilibrium landscape to a single equilibrium. With numerical simulations we illustrate the effectiveness of our approach in stabilizing the closed-loop system around this unique equilibrium, which falls in a neighborhood of the toggle switch unstable equilibrium, if the controller parameters are properly tuned.