Time delays in the feedback loop complicate the analysis and design of the closed-loop system. The use of a Smith predictor in combination with a Proportional Integral Derivative (PID) controller is a well-known technique for dealing with these delays in stable systems. In this paper, a graphical method is introduced for finding all stabilizing PID controllers that satisfy a robust performance constraint for any arbitrary order stable transfer function with time delay when a Smith predictor is used. The use of a Smith predictor tends to increase the size of the set of all PID controllers that satisfy the robust performance constraint in the controller parameter space. A numerical example is used to compare the set of PID controllers with and without a Smith predictor.