Approximations of the globally optimal nonlinear quadratic regulator (NQR) strategy are employed to control the unstable steady state of a continuous stirred tank reactor. It is shown that the proposed approximate NQR controllers can be uniquely determined through solution of Riccati and linear matrix equations and can deliver better dynamic performance than the linear quadratic regulator (LQR) if the process model is proper. Stability, optimality, and constraint satisfaction regions for these controllers are identified.