In this paper a method of adaptive continuous-time controller design for the control of a continuous stirred tank reactor is presented. The controlled output of the reactor is the reactant temperature, the control input is the coolant flow rate. The control is based on the choice of an external model of the controlled system with recursively estimated parameters. The pole location of the closed-loop transfer function is found through an LQ criterion minimisation. For controller design, the polynomial equation approach is adopted. Simulation results of reactor control, at prescribed operating conditions, are included.