The stabilization problem of third-order, time-delay unstable linear systems is analyzed. The systems under consideration have one unstable and two stable poles, which may be complex conjugate. Necessary and sufficient conditions to guarantee the stability of the closed loop system by means of a static output feedback are provided. Using such conditions, a predictor scheme that improves the transient system performance is proposed. To illustrate the application of the proposed strategy, it is applied to an unstable continuously stirred tank reactor model. Simulation results are presented.