In this paper a globally stabilizing boundary feedback control law for an arbitrarily fine discretization of a nonlinear PDE model of a chemical tubular reactor is presented. The objective is to stabilize an unstable steadyûstate of the system using boundary control of temperature and concentration on the inlet side of the reactor. We discretize the original nonlinear PDE model in space using finite difference approximation and get a high order system of coupled nonlinear ODEs. Then, using backstepping design for parabolic PDEs we transform the original coupled system into two uncoupled target systems that are asymptotically stable in l₂-norm with appropriate homogeneous boundary conditions. In the real system the designed control laws would be implemented through small variations of the prescribed inlet temperature and prescribed inlet concentration.